Quantum mechanics

Control (management)

Discretization

Ecology

CHAOS (operating system)

Bifurcation

Biology

Statistics

Predation

Applied mathematics

Computer security

Predator

Stability (learning theory)

Synchronization of chaos

Computer science

Statistical physics

Saddle-node bifurcation

Biological applications of bifurcation theory

Physics

Nonlinear system

Mathematics

Discrete time and continuous time

Control of chaos

Mathematical analysis

Artificial intelligence

Uniqueness

Control theory (sociology)

Transcritical bifurcation

Machine learning

Communications in Nonlinear Science and Numerical Simulation

In this work, a discretized two-dimensional Leslie-Gower prey-predator model is investigated. The results for the existence and uniqueness and the conditions for the local asymptotic stability of the solutions are determined. It is also exhibited that the discrete system undergoes Neimark-Sacker, flip and fold bifurcation under certain conditions. The discretized system exhibits wide range of complex dynamical behavior viz. periodicity, quasi periodicity and chaos with respect to different parameters. Further, three control methods: state feedback, pole-placement and hybrid control are deployed to control the chaos in the system. Under certain conditions, chaos and bifurcation of the system are stabilized through the control strategies. The extensive numerical simulation is done to demonstrate the analytical findings.

Dynamical analysis and chaos control in discrete-time prey-predator model