Flip and Neimark-Sacker Bifurcations in a Coupled Logistic Map System

TL;DR

This paper analyzes a coupled logistic map system, identifying and classifying bifurcations such as flip and Neimark-Sacker, using both theoretical and numerical methods to understand its stability and dynamics.

Contribution

The study provides a detailed bifurcation analysis of a coupled logistic map system, highlighting the existence of reverse flip and Neimark-Sacker bifurcations with combined theoretical and numerical approaches.

Findings

Existence of reverse flip bifurcations

Presence of Neimark-Sacker bifurcations

Stability classification of fixed points

Abstract

In this paper we consider a system of strongly coupled logistic maps involving two parameters. We classify and investigate the stability of its fixed points. A local bifurcation analysis of the system using Center Manifold is undertaken and then supported by numerical computations.This reveals the existence of reverse flip and Neimark-Sacker bifurcations.