Complex Dynamics of a Discrete-Time Prey–Predator System with Leslie Type: Stability, Bifurcation Analyses and Chaos

Abstract

Dynamic behavior of a discrete-time prey–predator system with Leslie type is analyzed. The discrete mathematical model was obtained by applying the forward Euler scheme to its continuous-time counterpart. First, the local stability conditions of equilibrium point of this system are determined. Then, the conditions of existence for flip bifurcation and Neimark–Sacker bifurcation arising from this positive equilibrium point are investigated. More specifically, by choosing integral step size as a bifurcation parameter, these bifurcations are driven via center manifold theorem and normal form theory. Finally, numerical simulations are performed to support and extend the theoretical results. Analytical results show that an integral step size has a significant role on the dynamics of a discrete system. Numerical simulations support that enlarging the integral step size causes chaotic behavior.

Stability and bifurcation analysis of a discrete Leslie predator-prey model with fear effect

“…Discrete-time models provide the most precise depiction of the dynamics shown by animals that participate in seasonal reproduction and have nonoverlapping generations. In addition, discrete models exhibit much more complicated dynamical patterns as compared to continuous-time models [1,2,5,14,19,29,30,44]. Thus, discrete-time models are more appealing than continuous ones.…”

Behavior Analysis of a Class of Discrete-Time Dynamical System with Capture Rate

“…In the past few years, many studies have shown that discrete-time predator-prey systems have more abundant dynamic behaviors than continuous systems, such as bifurcation and chaos. They have obtained the relevant dynamic behaviors among populations through numerical simulation [17][18][19][20][21][22][23][24].…”

Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response

“…Santra et al [14] investigated bifurcation and chaos of a discrete predator-prey model with Crowley-Martin functional response. For more dynamical investigations related to different versions of prey-predator models, we refer to Baydemir et al [15], Santra et al [16], Rech [17], Singh and Deolia [18], Khan and Khalique [19,21], Rozikov and Shoyimardonov [20] and references therein.…”