Jai Prakash Tripathi

Stability analysis of two prey one predator model

In this paper we study a two prey one predator model with team approach. We analyze local stability behaviour of the system with the help of linearization and persistence behaviour of the system with the help of persistence of all three teams individually.

Almost Periodicity of a Modified Leslie–Gower Predator–Prey System with Crowley–Martin Functional Response

In this paper, we discuss a modified Leslie–Gower Lotka–Volterra system with Crowley–Martin type functional response. Crowley–Martin functional response is similar to the Beddington–DeAngelis functional response but contains an extra term describing mutual interference by predators at high prey density. The rates are assumed to be almost periodic, which generalizes the concept of periodicity. We discuss the permanence, existence, uniqueness, and asymptotic stability of an almost periodic solution of the model under consideration by applying comparison theorem of differential equations and constructing a suitable Lyapunov functional. The analytical results obtained in this paper are illustrated with the help of a numerical example.

A Non-autonomous Ecological Model with Some Applications

Here, we propose a non-autonomous predator–prey system with feedback controls. Some of its possible applications in some branches of advanced computing have also been discussed. In particular, the global attractivity of the almost periodic solution (APS) is proved. The effect of control parameters has also been observed. The paper ends with some current possible applications of the work in bioinformatics, social networks, wireless sensor networks (WSNs), etc.

Global dynamics and parameter identifiability in a predator-prey interaction model

Abstract This paper discusses a predator-prey model with prey refuge. We investigate the role of prey refuge on the existence and stability of the positive equilibrium. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional, which shows that the prey refuge has no influence on the permanence property of the system. Mathematically, we analyze the effect of increase or decrease of prey reserve on the equilibrium states of prey and predator species. To access the usability of proposed predator-prey model in practical scenarios, we also suggest, the use of Levenberg-Marquardt (LM) method for associated parameter estimation problem. Numerical results demonstrate faithful reconstruction of system dynamics by estimated parameter by LM method. The analytical results found in this paper are illustrated with the help of suitable numerical examples

Interaction between prey and mutually interfering predator in prey reserve habitat: Pattern formation and the Turing–Hopf bifurcation

Abstract In this paper, we propose a diffusive prey-predator system with mutually interfering predator (Crowley–Martin functional response) and prey reserve. In particular, we develop and analyze both spatially homogeneous model based on ordinary differential equations and reaction-diffusion model. We mainly investigate the global existence and boundedness of positive solution, stability properties of homogeneous steady state, non-existence of non-constant positive steady state, conditions for Turing instability and Hopf bifurcation of the diffusive system analytically. Conventional stability properties of the non-spatial counterpart of the system are also studied. The analysis ensures that the prey reserve leaves stabilizing effect on the stability of temporal system. The prey reserve and diffusive parameters leave parallel impact on the stability of the spatio-temporal system. Furthermore, we illustrate the spatial patterns via numerical simulations, which show that the model dynamics exhibits diffusion controlled pattern formation by different interesting patterns.

A Delayed Non-autonomous Predator-Prey Model with Crowley-Martin Functional Response

In this work, we propose a delayed non-autonomous prey-predator system with Crowley-Martin functional response (CMFR). Mutual interference by predators at high prey density differentiate between Beddington-DeAngelis functional response and CMFR. We discuss the permanence, extinction, stability, existence and uniqueness of a globally attractive almost periodic solution (APS). In addition to effect of Crowley-Martin parameter, we also show that the intrinsic growth rate leaves positive effect on the permanence of the considered model system. Some numerical examples are also presented to support obtained analytical results.