Doctor of Philosophy, The Ohio State University, 2020, Electrical and Computer Engineering

DC distribution networks have found increased applications in electric automobiles, ships, aircrafts, server farms, and EV charging stations. These networks contain load regulating power electronic converters such as dc-dc and dc-ac converters that act as Constant Power Loads (CPLs). When these CPLs interact with the dc system, they can cause destabilizing effects on the grid due to their negative incremental impedance. Preliminary studies have performed stability analysis of dc distribution systems and proposed passive stabilization and source/load converter level controlstrategies to address the instability issue which does not address all the stability issues of multi-terminal dc distribution systems. In this research, a method to dynamically stabilize CPLs at the point of load by making them behave as adaptive Smart Resistors using high bandwidth power converters and energy storage units has been proposed. By utilizing high bandwidth power converters, these Smart Resistors can work with smart sources to realize ultimate intelligent power networks. This research aims to identify the realization of the smart Resistor concept and its utilization in the control of dc distribution systems. The effect of the Smart Resistor on the stability of various configurations of dc distribution networks are studied. The aims of this research study are as follows: The control strategies needed to achieve the Smart Resistor concept. The trajectory control of the system during voltage and current transients are studied. The energy management of energy storage is also proposed. The interaction of a constant power load powered by an ideal voltage source and a case study of a traction drive system is performed and the small and large-signal stability of the system is analyzed. The stability of a non-ideal source power converter feeding a constant power load. A case study of a section of a turbo-electric aircraft is used to showcase how the CPL (open full item for complete abstract)

Master of Science in Engineering (MSEgr), Wright State University, 2013, Electrical Engineering

Complex cyber-physical systems are difficult to model and control. However, humans are capable of accomplishing these tasks by constantly adapting and redefining the rules to control these complex systems. Fuzzy logic provides a means of encoding human inference into a control methodology. However, the fuzzy logic controllers are nonlinear and their stability is difficult to verify. Therefore, the widespread usefulness of fuzzy logic controllers is limited. It has been proven that fuzzy logic controllers can be implemented as piecewise linear switched controllers. It has also been shown that the piecewise linear system can be implemented as a hybrid system. Piecewise linear hybrid system stability can be verified by extending the Lyapunov proof for one linear system to multiple decreasing Lyapunov functions. The objective of this thesis is to implement fuzzy logic control systems as a piecewise linear hybrid system and examine their stability. A proportional fuzzy logic controller with constant derivative gain is implemented as a piecewise linear hybrid system using Matlab Simulink Stateflow. Stability of the system is examined by obtaining the Lyapunov function of each subsystem and stitching them according to the fuzzy rules. It is shown that the stitching of Lyapunov functions must successively decrease for the system to be stable. Further implications of robustness are examined by varying the fuzzy logic rules and observing the effect on the corresponding stitched Lyapunov functions.

Doctor of Philosophy, The Ohio State University, 2024, Mechanical Engineering

To meet the growing demands of electric vehicles and energy storage devices, it is essential to develop advanced lithium-ion batteries (LIBs) that not only provide high energy density but also affordability and rapid charging and discharging capabilities. Cathode materials account for over 40% of the total cost of a battery and directly determine the battery's voltage and capacity. Therefore, it is imperative to develop low-cost cathode materials with high electrochemical performance. In this dissertation, we explored several cobalt-free cathode materials, including spinel-structured LiNi0.5Mn1.5O4 (LNMO), nickel-rich cobalt-free LiNi0.95M0.05O2 (M=Al, Mn, Mg, and Ti) layered oxides and xLi2MnO3·(1 – x)LiMO2 (M = Ni and Mn) layered oxides (LMR), which have the advantage of low raw materials price compared to commercialized cathode materials, such as LiCoO2 and cobalt-rich LiNi0.33Co0.33Mn0.33O2 (NMC111) layered oxides. However, like most cathode materials, they also encounter significant challenges, including low thermal stability, an unstable internal structure, and rapid capacity fading, which is caused by serious anisotropic volume changes during cycling, continuous electrolyte decomposition, and transition metal dissolution, particularly at high operating voltages. To overcome these challenges, we present three advanced strategies aimed at producing intergranular-crack-free cathode materials with superior cycling performance, high internal structure stability, and minimal parasitic reactions even under severe cycling conditions. Firstly, employing solid-state electrolytes as Li-ion conductors to form a stable cathode electrolyte interphase (CEI) layer. Secondly, establishing a concentration-gradient layered oxide with a Ni-rich core and an enrichment of substituted elements in the surface region through a co-precipitation reactor. The presence of a Ni-rich core enhances the material's capacity, while the transition elements at the surface ensure excellent cycla (open full item for complete abstract)

Doctor of Philosophy (PhD), Ohio University, 2024, Mathematics (Arts and Sciences)

The Lyapunov stability of equilibria in dynamical systems is determined by the interplay between the linearization and the nonlinear terms. In this work, we study the case when the spectrum of the linearization is diffusively stable with high-order spectral degeneracy at the origin. In particular, spatially periodic solutions called roll solutions at the zigzag boundary of the Swift-Hohenberg equation (SHE), typically selected by patterns and defects in numerical simulations, are shown to be nonlinearly stable. This also serves as an example where linear decay weaker than classical diffusive decay, together with quadratic nonlinearity, still gives nonlinear stability of spatially periodic patterns. The study is conducted on two physical domains: the 2D plane, $\R^2$, and the cylinder, $T_{2\pi}\times \R$. Linear analysis reveals that instead of the classical $t^{-1}$ diffusive decay rate, small localized perturbation of roll solutions with zigzag wavenumbers decay with slower algebraic rates ($t^{-\frac{3}{4}}$ for the 2D plane; $t^{-\frac{1}{4}}$ for the cylindrical domain) due to the high order degeneracy of the translational mode at the origin of the Bloch-Fourier spaces. The nonlinear stability proofs are based on decompositions of the neutral translational mode and the faster decaying modes, and fixed-point arguments, demonstrating the irrelevancy of the nonlinear terms.

Doctor of Philosophy, University of Toledo, 2023, Exercise Science

Athletic populations commonly suffer from various injuries to the back, hip, and knee. Common risk factors, often in the form of movement patterns or strength deficits, have been identified for injuries that negatively impact sport performance or the ability to participate in sport. These common risk factors may be suggestive of a proximal cause-the lumbopelvic-hip complex (LPHC). The LPHC is the center of the kinetic chain and is important for optimal force generation and distribution to the lower extremity during athletic movements. LPHC stability can be defined as the ability of the trunk to maintain optimal positioning over the pelvis and lower extremity in the presence of perturbations. Additionally, LPHC stability can be considered the combined muscular strength, endurance, and sensorimotor control of the muscles and fascia within the complex. Deficits in LPHC stability have been related to movement patterns that are related to increased injury risk and incidence of injury. The proposed connections between LPHC stability and injury risk prompt recommendations for inclusion of LPHC stability training in injury prevention efforts. To better understand the emphasis that should be placed on LPHC stability training for the purpose of injury prevention or rehabilitation, it is important to further investigate the mechanisms by which LPHC stability relates to injury risk factors, and whether improving LPHC stability results in relevant functional changes. Our population of interest included university club sport athletes who are regularly at risk for injury due to their participation in sport, but represents a more recreational population that commonly do not have access to outside training regimens or clinical interventions. In manuscript 1, we explored the relationships between clinical measures of LPHC stability, trunk kinematics, and the margin of stability during landing tasks. Because the head, arms, and trunks make up 70% of the body's mass, control of trunk m (open full item for complete abstract)

Master of Science, University of Toledo, 2023, Mathematics

Throughout time, throughout the world, epidemic diseases have depleted whole cultures, changed history and been one of the most significant threats to human survival. Medicine and government have worked to limit the spread of and reduce the severity of diseases. Mathematics has been an able partner in that fight. Through the use of modeling, mathematics has been able to provide the medical community and civic authorities with information on size, severity, and spread of the disease. This paper presents the development of some key epidemic models, investigates properties of the solutions, and discusses the stability of the disease-free and endemic equilibriums. The Threshold theorem developed by Kermack-McKendrick is derived and the calculation of the reproduction number, R_0 is performed. The reproduction number predicts the average number of secondary infections caused by a lone infected individual in a population composed of all susceptible people. The reproduction number depends on the rate of transmission, Beta, the rate of recovery, gamma, and the size of the susceptible population, S. This paper clearly demonstrates the calculation of the reproduction number which is beneficial for any mathematician desirous of using the reproduction number to study infectious diseases and investigate the impact of various disease-fighting tools.

PhD, University of Cincinnati, 2021, Arts and Sciences: Chemistry

The outline of this dissertation is achieving higher selectivity by controlling the photoreactivity. We report the selective formation of the targeted photoproducts by controlling the photoreactivity of 2-hydroxy chalcone derivatives as well as different types of organic azides. In addition, we explored the photoreactivity under continuous flow method and in cryogenic matrices as well. Below is a summary of the research projects explored and studied in this dissertation, ?

Master of Science, University of Akron, 2020, Polymer Engineering

The present thesis focuses on elucidation on the role of ionic liquid in polymer electrolyte membranes for energy harvesting and storage. Recently, research interest on ionic liquid-in-salt has gained considerably due to its high thermal stability and ionic conductivity, which has potential as a replacement for the facile organic solvent electrolyte in lithium ion battery. The status of emerging lithium ion batteries has been reviewed in Chapter I, followed by Materials and Methods including physical and electrochemical characterizations in Chapter II and Chapter III. In Chapter IV, the polymer electrolyte membrane (PEM) containing liquid polyether sulfide (PES, Thiokol) was fabricated via thiol-ene click reaction with poly (ethylene glycol) diacrylate (PEGDA) with the aid of a photo-initiator under UV light for photocuring. The so-called solid polymer electrolyte membrane thus formed is an isotropic, completely amorphous, transparent, and flexible solid-state membrane. The ionic conductivity of (PES-co-PEGDA/HMIMTFSI) was determined by AC impedance as a function of thiol (SH) content which served as flexible side chains. The ionic liquid (HMIMTFSI) can dissociate Li ions from its salt and also plasticize the PEM network. As a result, the increasing amount of Thiokol and HMIMTFSI can both sevred as the ionizers to enhance the ionic conductivity. The flexoelectric coefficients (μ) of various PEMs-(TK-co-PEGDA/HMITFSI) were determined under intermittent square wave and dynamic oscillatory bending modes by using Dynamic Mechanical Analyzer (DMA) combined with Solartron Potentiostat/Galvanostat. The present PEM (TK-co-PEGDA/HMIMTFSI) exhibited larger flexoelectric coefficient than those of conventional insulating materials such as ferroelectric ceramics and bent-core nematic liquid crystals. Last not least, the efficiency of mechano-electrical energy conversion the PEM (TK-co-PEGDA/HMITFSI) is discussed. Chapter V addresses the mutual solubility of ionic liquid (IL) (open full item for complete abstract)

Doctor of Philosophy, University of Akron, 2020, Engineering-Applied Mathematics

A model is developed for predicting long-wavelength film thickness nonuniformities in drying latex paint films. After applying the lubrication approximation to the model equations, both linear and nonlinear stability analyses are performed. For the linear stability analysis, spatially independent base state solutions are found. These equations are solved numerically and a linear stability analysis of these base state solutions is conducted. In this case, the base state solution of the height represents a uniformly drying latex paint film with respect to time. For the nonlinear stability analysis, the leading order equations are solved numerically. The stability of the film is dependent on temperature, latex particle volume fraction, titanium dioxide particle volume fraction, extender particle volume fraction, surface surfactant density, bulk surfactant density, and several material and environmental factors. Slow evaporation, temperature gradients, surfactant desorption, surface tension gradients, low initial surface tension are identified as destabilizing mechanisms while fast evaporation, fast surfactant adsorption, high initial surface tension, high particle volume fractions, and viscosity are identified as stabilizing mechanisms.

Doctor of Philosophy, The Ohio State University, 2019, Electrical and Computer Engineering

The first part of this dissertation extends the applicability of stability-preserving mappings to dynamical systems whose evolutionary processes explicitly consider the effect of external perturbations (inputs) and measurements (outputs), via multi-valued operators. We provide definitions for input-to-state stability and input-to-output stability for a general class of systems whose trajectories lie in arbitrary metric spaces, indexed by hybrid time sets. Novel proofs of results such as the ISS-Lyapunov and the small-gain theorem are developed with the use of stability-preserving mappings. The second part, where we employ the theory to model and analyze the complex dynamics found in the interplay of the determinants of mood disorders. The model integrates biopsychosocial findings of the bipolar and depressive spectra, modeling attractors corresponding to mood states such as euthymia, mania, depression, the mixed state, anhedonia, hedonia, and flat or blunted affect, as well as the transitions among these attractors caused by external influences, like stress and medication. Conditions for global stability of euthymia, obtained via a stability analysis, are supported by studies in the neuropsychology literature, while computational analyses provide a novel explanation of the mechanism underlying mood stabilizers.

PhD, University of Cincinnati, 2017, Education, Criminal Justice, and Human Services: Criminal Justice

Since place-based crime has been studied, scholars have employed a variety of ways to describe the concentration of crime at places. Most usefully, they sometimes provide a full distribution of crime across street segments, or among addresses, or other small geographic areas of interest. This is feasible if the researcher is showing the distribution of crime at places throughout one or two larger areas, such as a city. In such circumstances, a few tables or graphs will be sufficient. But once researchers started looking at spatial areas numbering in the hundreds and thousands, like street segments, then describing the internal distribution of crime within each becomes cumbersome. We need summary measures of crime concentration. The mean, median, and mode are not appropriate for this task: the first two because of the highly skewed nature of crime distributions, and while the mode is better, it does not provide enough information.

Doctor of Philosophy, The Ohio State University, 2017, Mechanical Engineering

Many control system applications are undergoing a transition from digital control to networked control, similar to the transition from analog several decades ago. Networked control eases the process of utilizing information across distributed locations or other obstacles. Some industries that have begun to make use of networked control include automotive, aerospace, manufacturing, and internet based controllers. This dissertation draws specific motivation from the aerospace industry, where both geographic and size considerations are important considerations. Networked control systems (NCSs) have unique considerations that require further research, including delay, uncertainty, and bandwidth constraints. All three of these are addressed in this dissertation in addition to further control topics. First, in many previous papers, only a single delay has been considered in NCSs. This assumption ignores the distributed nature of sensors and actuators in a NCS, where there is likely an independent delay between the controller and each connected node. Delays are addressed in this dissertation by providing a new formulation that compactly models time-varying independent delays for each sensor and actuator. Second, uncertainty is addressed from the likely source, the continuous-time domain. Because NCSs interacting with physical systems are inherently sampled-data systems, model-based control generally starts with the continuous-time model. This dissertation considers a perturbation on the continuous-time plant model, bounding the size that still meets the performance specifications. Two different approaches are given. The first is robust stability that assumes the desired performance is for the system to be stable. To comprehensively address NCSs, several new theorems with a new extension allowing for time-varying systems, are presented for delay-free discrete-time systems and delay free, single lumped-delay, multiple delay (MD), and estimator compensated MD sampled-da (open full item for complete abstract)

Doctor of Philosophy, The Ohio State University, 2016, Aero/Astro Engineering

The use of thin-gauge, light-weight structures in combination with the severe aero-thermodynamic loading makes reusable hypersonic cruise vehicles prone to fluid-thermal-structural interactions. These interactions result in surface perturbations in the form of temperature changes and deformations that alter the stability and eventual transition of the boundary layer. The state of the boundary layer has a significant effect on the aerothermodynamic loads acting on a hypersonic vehicle. The inherent relationship between boundary-layer stability, aerothermodynamic loading, and surface conditions make the interaction between the structural response and boundary-layer transition an important area of study in high-speed flows. The goal of this dissertation is to examine the interaction between boundary layer transition and the response of aerothermally compliant structures. This is carried out by first examining the uncoupled problems of: (1) structural deformation and temperature changes altering boundary-layer stability and (2) the boundary layer state affecting structural response. For the former, the stability of boundary layers developing over geometries that typify the response of surface panels subject to combined aerodynamic and thermal loading is numerically assessed using linear stability theory and the linear parabolized stability equations. Numerous parameters are examined including: deformation direction, deformation location, multiple deformations in series, structural boundary condition, surface temperature, the combined effect of Mach number and altitude, and deformation mode shape. The deformation-induced pressure gradient alters the boundary-layer thickness, which changes the frequency of the most-unstable disturbance. In regions of small boundary-layer growth, the disturbance frequency modulation resulting from a single or multiple panels deformed into the flowfield is found to improve boundary-layer stability and potentially delay transition. For (open full item for complete abstract)

Doctor of Philosophy (PhD), Ohio University, 2016, Civil Engineering (Engineering and Technology)

Sedimentation is one of the important factors affecting stream channel stability. The estimation of sediment supply, assessment of channel stability, and potential influencing factors are of interest in this study. A proposed model was developed by the integration of Revised Universal Soil Loss Equation (RUSLE) model and Watershed Assessment of River Stability and Sediment Supply (WARSSS), aiming to estimate the sediment load and evaluate the channel stability of a man-made channel. The proposed model was applied to the channelized Hocking River near Athens, Ohio. It was estimated that the annual gross erosion from the watershed was 728,733,738 kg, 97% of which was from the surface erosion, while only 3% resulted from streambank erosion. The total sediment yield in the channelized Hocking River was indirectly estimated by the addition of suspended sediments and bedload sediments, which were directly measured in the channel. The total annual sediment yield was 80,991,718 kg, in which 98% was estimated from suspended sediments and 2% from bedload sediments. This resulted in a sediment delivery ratio of 11%, which was consistent with those of the watersheds having similar size in the studied region. The total sediment transport capacity was estimated by the proposed model to be 17,161,761 kg/yr. Compared with the total sediment yield of 80,991,718 kg, 21% of which was transported by the river flow. The majority of sediments deposited in the channel due to the insufficient transport capacity. The amount of sediment accumulated was indirectly verified by the annual dredging project conducted by the Hocking Conservancy District (HCD). The channel stability of the Hocking River near Athens, Ohio was assessed by the characteristics of soil erosion for each monitored reach. Based on the four categories of stability determinations, most of the studied reaches were unstable in the lateral direction and all the reaches had excess deposition except one of the downstream r (open full item for complete abstract)

Doctor of Philosophy, The Ohio State University, 2015, Electrical and Computer Engineering

In recent years, there has been a great interest in wide-band small antennas for wireless communication in both ground and airborne applications. Electrically small antennas; however, are narrow bandwidth since they exhibit high a quality factor (Q). Therefore, matching networks are required to improve their input impedance and radiation characteristics. Unfortunately, due to gain-bandwidth restrictions, wideband matching cannot be achieved using passive networks unless a high order matching network is used. Fortunately, the so-called non-Foster circuits (NFCs) employ active networks to bypass the well-known gain-bandwidth restrictions derived by Bode-Fano. Although NFCs can be very useful in numerous microwave and antenna applications, they are difficult to design because they are potentially instable. Consequently, an accurate and efficient systematic stability assessment is necessary during the design process to predict any undesired behavior. In this dissertation, the design, stability, and measurement of two non-Foster matching networks for two different small monopole antennas, a non-Foster circuit embedded within half loop antenna, a combination of Foster and non-Foster matching network for small monopole antenna are presented. A third circuit; namely, a non-Foster coupling network for a two-element monopole array is also presented for phase enhancement applications. It all examples, the NFCs substantially improve the antenna's performance over a wide frequency band. First, the stability properties of NFCs are discussed with a time-domain technique that computes the largest Lyapunov exponent for time series signals. In case of instability, it is shown how the circuit can be stabilized with different controllers. The proposed stability approach has been successfully applied to a negative capacitor to match a 3" electrically small monopole receiver antenna. Measured results verified that the system is stable and the non-Foster matching networks improve bot (open full item for complete abstract)

Master of Science, The Ohio State University, 2015, Mechanical Engineering

The problem considered is the robustness of a system stabilized by a discrete controller under state feedback with time delay. The ability to guarantee certainty of stability when the system is uncertain falls in the domain of robust control. Historically, robustness bounds have been formulated for net uncertainty ranges of the resulting overall system. These robustness bounds are state dependent and change with selection of states of the system. Recent new work has reformulated bounds in terms of uncertainty in the plant which originates system uncertainty not only by itself but also by affecting the state feedback and sampling as well. Results have been presented which demonstrate state selection variance for the case of plant uncertainty in order to possibly obtain better robustness bounds. Methods to implement such change of states and conditions for favorable state transformation are discussed. The methods are applied to cases studied in the past to document superior bounds. Finally, results are presented for state transform in the case of disturbances that has a known form based on previous work on perturbations with known structure.

Master of Science, University of Akron, 2014, Polymer Engineering

Binary and ternary phase diagram of poly(ethylene glycol) dimethacrylate (PEGDMA), bis(trifluoromethane)sulfonimide (LiTFSI), and succinonitrile (SCN) blends have been established by means of differential scanning calorimetry and polarized optical microscopy. The binary phase diagram of PEGDMA/SCN mixture is of typical eutectic type, whereas the binary phase diagram of PEGDMA/LiTFSI mixture exhibits a wide single-phase region at the intermediate compositions. The ternary phase diagram of PEGDMA/SCN/LiTFSI mixture shows a wide isotropic region. The polymer electrolyte membrane (PEM), which is formed by ternary blends in this region after UV-crosslinking, remains in the isotropic phase and performs. The room temperature ion conductivity as evidenced in AC impedance measurement, was found to be extremely high (i.e., 10-3 S/cm). This ionic conductivity increases to 10-2 S/cm at 60 °C that continues to improve further up to 135 °C investigated. More importantly, the high ionic conductivity behavior is reproducible in repeated heating/cooling cycles. Those PEM are solid-state, stretchable, nonflammable, and light weight, which may be applicable to lithium ion battery as a replacement of commercial liquid electrolyte. SCN in ternary blends affords not only dissociation of the lithium salt, but also plasticization to the cross-linked PEGDMA network. Last not least, thermal and electrochemical stability of these membranes were examined for further application probability.

B.S. in Exercise Science, University of Toledo, 2009, Exercise Science

Dynamic balance is a key component of normal daily activities such as walking, running and climbing stairs. Since balance is such an important aspect of every day life, it is imperative to find programs useful for maintaining proper balance. One such suggestion that has been made in an effort to improve balance is the correlation between muscular strength training and enhanced balance. Training the core muscles especially has been hypothesized as an improvement program, but there is a lack of current scientific evidence to support this claim. Further investigation on the effect of a core stability program on balance is therefore needed in a effort to provide a balance maintenance program. Therefore, this study sets out to compare the effects of a core stability program on dynamic balance as measured with the Star Excursion Balance Test.Thirty participants (15 male, 15 female) with no known musculoskeletal injuries or neurologic deficits volunteered for the study. The participants were randomly divided into two groups, a control group and an exercise group. The control group performed an initial Star Excursion Balance Test followed by six weeks of no core strengthening exercises and a second Star Excursion Balance Test. The exercise group performed the first Star Excursion Balance Test followed by six weeks of a core stability program and a second Star Excursion test. The maximum excursion distances as normalized to leg length were recorded for each test. For a majority of the reach directions, maximum excursion distances improved for the exercise group when compared to the control group. This improvement in reach distance justifies the proposal of core strengthening improving dynamic postural control.

MS, University of Cincinnati, 2006, Engineering : Electrical Engineering

Prediction and prevention of falls is a very important part of creating safe and productive workplaces. The risk of falling during workplace activity is related to postural stability. However, assessing postural stability during task performance is difficult and expensive because the task conditions used in testing themselves trigger slips, necessitating the use of strict protocols and protective equipment whereas it would be easier to get data from upright standing static position. Also, using data from such dynamic tests is problematic because the movement of the subjects is likely to make it even more non-stationary than data obtained under static conditions . Thus the research proposed here considers the possibility of using postural data obtained under much simpler static testing conditions to predict postural stability during dynamic workplace tasks.

Doctor of Philosophy, The Ohio State University, 2011, Mathematics

We utilize reaction-diffusion-advection equations in an adaptive dynamic framework to study the evolution of dispersal of two competing species. The species are assumed to be identical except for their dispersal strategies which consist of random movement (diffusion) and biased movement (advection) upward along resource gradients. We focus on how spatial heterogeneity in the habitat influences selection. A key facet of this relationship is that diffusion creates a mismatch between a species population density at steady state and the resource function [9]. This led Cantrell et al. [9] to introduce a conditional strategy which can perfectly match the resource, resulting in the ideal free distribution of the species at equilibrium. This ideal free strategy (IFS) serves as a basis for our study. Not only do we show that it is a global evolutionarily stable strategy, but we find conditions under which it is convergent stable, varying random dispersal rates, advection rates, or both of these parameters at the same time. For two similar strategies on the "same side" of the IFS we show that when resource function is monotone, the strategy which is closer to the IFS is generally selected. For nonmonotone resource functions, we find that there may exist nonideal free strategies which are locally evolutionarily stable and/or convergent stable [21]. In addition, we find that for certain nonmonotone resource functions, two similarly competing species can coexist, which enables us to also show how three species coexistence is possible.