Abstract In the present work, a system of two linear coupled logistic map is studied. Local stability analysis of the fixed points of the proposed system is investigated. The system occurs transcritical, flip, and Neimark-Sacker bifurcations, which are analyzed by both center manifold theory and bifurcation theory. For any non-linear system that represents a real-world model affected by noise, white noise is included in the system and its effect on fixed points is analyzed via the technique of stochastic sensitivity function. The phenomenon of noise-induced transitions between closed invariant curves is discussed. Finally, numerical simulations are performed with the aid of Matlab to assure the agreements with analytical results obtained.
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