Existence of Forced Waves and Their Asymptotic for Leslie-Gower Prey-Predator Model with Nonlocal Effects under Shifting Environment

In this paper, we prove the existence of forced waves for Leslie-Gower prey-predator model with nonlocal effects under shifting environment. By constructing a pair of upper and lower solutions with the method of monotone iteration, we can obtain the existence of forced waves for any positive constant shifting speed. Finally, we show the asymptotical behavior of traveling wave fronts in two tails.

DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL

In this article,we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model,which describes the interaction bet ween populations of prey and predator,and takes into account the economic interest.We firstly obtain the solvability condition and the st ability of the model sys tem,and discuss the singularity induced bifurcation phenomenon.Next,we introduce a st ate feedback controller to elimina te the singularity induced bifurcation phenomenon,and discuss the optimal control problems.Finally,numerical solutions and their simulations are considered in order to illustrate the theoretical results and reveal the more complex dynamical behavior.

Global existence of weak solutions to a prey-predator model with strong cross-diffusion

Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.

Chaos Behavior and Estimation of the Unknown Parameters of Stochastic Lattice Gas for Prey-Predator Model with Pair-Approximation

In this paper, the problem of chaos, stability and estimation of unknown parameters of the stochastic lattice gas for prey-predator model with pair-approximation is studied. The result shows that this dynamical system exhibits an oscillatory behavior of the population densities of prey and predator. Using Liapunov stability technique, the estimators of the unknown probabilities are derived, and also the updating rules for stability around its steady states are derived. Furthermore the feedback control law has been as non-linear functions of the population densities. Numerical simulation study is presented graphically.

Study of Fractional Order Tri-Tropic Prey-Predator Model with Fear Effect on Prey Population

In this manuscript, we have studied a fractional-order tri-trophic model with the help of Caputo operator. The total population is divided into three parts, namely prey, intermediate predator and top predator. In addition, the predator fear impact on prey population is suggested in this paper. Existence and uniqueness along with non-negativity and boundedness of the model system have been investigated. We have studied the local stability at all equilibrium points. Also, we have discussed global stability and Hopf bifurcation of our suggested model at interior equilibrium point. The Adam-Bashforth-Moulton approach is utilized to approximate the solution to the proposed model. With the help of MATLAB, we were able to conduct graphical demonstrations and numerical simulations.

Fractional order prey-predator model incorporating immigration on prey:Complexity analysis and its control

In this paper,the Caputo fractional derivative is assumed to be the prey-predator model.In order to create Caputo fractional differential equations for the prey-predator model,a discretization process is first used.The fixed points of the model are categorized topologically.We identify requirements for the fixed points of the suggested prey-predator model's local asymptotic stability.We demonstrate analytically that,under specific parametric conditions,a fractional order prey-predator model supports both a Neimark-Sacker(NS)bifurcation and a Flip bifurcation.We present evidence for NS and Flip bifurcations using central manifold and bifurcation theory.The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order prey-predator model.As the bifurcation parameter is increased,the system displays chaotic behavior.Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations,phase portraits,invariant closed cycles,and attractive chaotic sets in addition to validating analytical conclusions.The suggested prey-predator dynamical system's chaotic behavior will be controlled by the OGY and hybrid control methodology,which will also visualize the chaotic state for various biological parameters.

Bifurcation Analysis of a Stage-Structured Prey-Predator System with Discrete and Continuous Delays

A three-stage-structured prey-predator model with discrete and continuous time delays is studied. The characteristic equations and the stability of the boundary and positive equilibrium are analyzed. The conditions for the positive equilibrium occurring Hopf bifurcation are given, by applying the theorem of Hopf bifurcation. Finally, numerical simulation and brief conclusion are given.

Mathematical Model for Two-Spotted Spider Mites System: Verification and Validation

This paper presents and compares four mathematical models with unique spatial effects for a prey-predator system, with Tetranychus urticae as prey and Phytoseiulus persimilis as predator. Tetranychus urticae, also known as two-spotted spider mite, is a harmful plant-feeding pest that causes damage to over 300 species of plants. Its predator, Phytoseiulus persimilis, a mite in the Family Phytoseiidae, effectively controls spider mite populations. In this study, we compared four mathematical models using a numerical simulation. These models include two known models: self-diffusion, and cross-diffusion, and two new models: chemotaxis effect model, and integro diffusion model, all with a Beddington-De Angelis functional response. The modeling results were validated by fitting experimental data. Results demonstrate that interaction scheme plays an important role in the prey-predator system and that the cross-diffusion model fits the real system best. The main contribution of this paper is in the two new models developed, as well as the validation of all the models using experimental data.

Positive Steady States of a Prey-predator Model with Diffusion and Non-monotone Conversion Rate

In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.

Positive solutions for a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-Ⅱ functional response

We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response.Here,a positive solution corresponds to a coexistence state of the model.Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane.In addition,we present the uniqueness of positive solutions in one dimension case.Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane.

Qualitative Analysis on a Reaction-Diffusion Prey-Predator Model and the Corresponding Steady-States

The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for non- existence of positive non-constant steady-states are derived.

Qualitative analysis on a diffusive prey-predator model with ratio-dependent functional response

In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.

STABILIZATION OF A KIND OF PREY-PREDATOR MODEL WITH HOLLING FUNCTIONAL RESPONSE

The stabilization problem of a kind of prey-predator model with Holling fimctional response is investigated. By approximate linearization approach, a feedback control law stabilizing the closed- loop system is obtained. On the other hand, by exact linearization approach, a suitable change of coordinates in the state space and a feedback control law render the complex nonlinear system to be a linear controllable one such that the positive equilibrium point of the closed-loop system is globally asymptotically stable.

Non-constant Stationary Solutions to a Prey-predator Model with Diffusion

In this paper, a nonlinear predator reproduction and prey competition model with diffusion is discussed. Some existence and non-existence results concerning non-constant positive steady-states are presented using topological degree argument and the energy method, respectively.

Existence, uniqueness and stability of positive steady states to a prey-predator diffusion system

In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.

Nontrivial Effect of Time-Varying Migration on the Three Species Prey-Predator System

Migration is ubiquitous in ecosystem and often plays an important role in biological diversity. In this work,by introducing a time-varying migration rate associated with the difference of subpopulation density into a prey, we study the Hopf bifurcation and the critical phenomenon of predator extinction of the three species prey-predator system,which consists of a predator, a prey and a mobile prey. It is found that the system with migration exhibits richer dynamic behaviors than that without migration, including two Hopf bifurcations and two limit cycles. Interestingly,the parameters of migration have a drastically influence on the critical point of predator extinction, determining the coexistence of species. Moreover, the population evolution dynamics of one-dimensional multiple prey-predator system are also discussed.

Artificial Neural Networks for Prediction of COVID-19 in Saudi Arabia

In this study,we have proposed an artificial neural network(ANN)model to estimate and forecast the number of confirmed and recovered cases of COVID-19 in the upcoming days until September 17,2020.The proposed model is based on the existing data(training data)published in the Saudi Arabia Coronavirus disease(COVID-19)situation—Demographics.The Prey-Predator algorithm is employed for the training.Multilayer perceptron neural network(MLPNN)is used in this study.To improve the performance of MLPNN,we determined the parameters of MLPNN using the prey-predator algorithm(PPA).The proposed model is called the MLPNN–PPA.The performance of the proposed model has been analyzed by the root mean squared error(RMSE)function,and correlation coefficient(R).Furthermore,we tested the proposed model using other existing data recorded in Saudi Arabia(testing data).It is demonstrated that the MLPNN-PPA model has the highest performance in predicting the number of infected and recovering in Saudi Arabia.The results reveal that the number of infected persons will increase in the coming days and become a minimum of 9789.The number of recoveries will be 2000 to 4000 per day.

Effects on prey-predator with different functional responses

In this paper, we investigate the effects on prey of two predators which are also related in terms of prey-predator relationship. Different types of functional responses are con- sidered to formulate the mathematical model for predator and generalist predator of our proposed model. Harvesting effort for the generalist predator is considered and the density-dependent mortality rate for predator and generalist predator is incorporated in our proposed model. Local stability as well as global stability for the system is dis- cussed. We analyze the different bifurcation parameters to evaluate Hopf bifurcation in the neighborhood of interior equilibrium point. Finally, some numerical simulations and graphical figures are provided to verify our analytical results with the help of different sets of parameters.

Novel Computing for the Delay Differential Two-Prey and One-Predator System

The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator system.The delay differential models are very significant and always difficult to solve the dynamical kind of ecological nonlinear two-prey and one-predator system.Therefore,a stochastic numerical paradigm based artificial neural network(ANN)along with the Levenberg-Marquardt backpropagation(L-MB)neural networks(NNs),i.e.,L-MBNNs is proposed to solve the dynamical twoprey and one-predator model.Three different cases based on the dynamical two-prey and one-predator system have been discussed to check the correctness of the L-MBNNs.The statistic measures of these outcomes of the dynamical two-prey and one-predator model are chosen as 13%for testing,12%for authorization and 75%for training.The exactness of the proposed results of L-MBNNs approach for solving the dynamical two-prey and onepredator model is observed with the comparison of the Runge-Kutta method with absolute error ranges between 10−05 to 10−07.To check the validation,constancy,validity,exactness,competence of the L-MBNNs,the obtained state transitions(STs),regression actions,correlation presentations,MSE and error histograms(EHs)are also provided.