Chaos of Exponential Logistic Map

In this paper, chaos of a new exponential logistic map modulated by Gaussian function is investigated. Firstly, the stability of the fixed point is analyzed, and the occurrence of period doubling bifurcation in the system is verified theoretically. Subsequently, the chaotic behavior of the system is analyzed using bifurcation diagrams, phase portraits, and Lyapunov exponents. The numerical results confirm the existence of chaos in the exponential logistic map within a specific parameter range. In addition, the proposed map has additional parameter degrees of freedom compared to the existing generalized logistic maps, which provides different chaotic characteristics and enhances design flexibility required for diverse applications. At last, we further study the two‐dimensional coupled exponential logistic map and find that the system enters chaos through two routes: period doubling bifurcation and Hopf bifurcation.