Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response

Abstract

The interaction between plants and herbivores is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of plants and herbivores interaction with non-overlapping generations, such that a new generation replaces the old at regular time intervals. Keeping in view the interaction of the apple twig borer and the grape vine, the qualitative behaviour of a discrete-time plant-herbivore model is investigated with weak predator functional response. The topological classification of equilibria is investigated. It is proved that the boundary equilibrium undergoes transcritical bifurcation, whereas unique positive steady-state of discrete-time plant-herbivore model undergoes Neimark-Sacker bifurcation. Numerical simulation is provided to strengthen our theoretical discussion. ARTICLE HISTORY

A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

“…It is easy to see that System (46) possesses a positive fixed point (H * , P * ) = (0.17236, 14.50693). On the other hand, the variational matrix for Equation (46) around (0.17236, 14.50693) is computed as follows:…”

“…Therefore, Hopf bifurcation is almost eliminated completely. Next, choosing α = 0.9995 plots for System (46) are shown in Figure 7. These plots reveal that the positive fixed point (0.17236, 14.50693) of System (46) is a sink (see Figure 7a-c).…”

“…On the other hand, chaos control methods are widely used in almost all branches of applied science [37]. For further details related to chaos control methods in discrete-time systems, we refer to [38][39][40][41][42][43][44][45][46][47][48].…”

A dynamically consistent nonstandard finite difference scheme for a predator–prey model

“…Recently, many iterated maps have been studied for existence and direction of Neimark-Sacker bifurcation (cf. [37][38][39][40][41][42][43][44][45][46][47][48][49][50]).…”

Dynamical Complexity in a Class of Novel Discrete-Time Predator-Prey Interaction With Cannibalism

“…Similarly, some discrete-time predator-prey models and hydra effect and paradox of enrichment are studied in [29]. Furthermore, for several attracting findings associated to the qualitative analysis of difference equations, we refer to the work done by [30], [31]. Also authors in [32] proposed and investigate the dynamics of cannibalism in discrete-time predator-prey system and considering twostage population model where cannibalism factor involving only in prey population.…”