Abstract
We introduce a discretization process to discretize a modified fractional-order optically injected semiconductor lasers model and investigate its dynamical behaviors. More precisely, a sufficient condition for the existence and uniqueness of the solution is obtained, and the necessary and sufficient conditions of stability of the discrete system are investigated. The results show that the system’s fractional parameter has an effect on the stability of the discrete system, and the system has rich dynamic characteristics such as Hopf bifurcation, attractor crisis, and chaotic attractors.
Highlights
The idea of fractional-order calculus (FOC) has been well known since the development of the regular calculus
The aim of this paper is to investigate the dynamical behavior of a discretization fractional order of a modified optically injected semiconductor lasers model
We introduced a fractional order of modified optically injected semiconductor lasers model and discretized this system by using a new discretization technique
Summary
The idea of fractional-order calculus (FOC) has been well known since the development of the regular calculus. Momani et al [23] applied the multistep generalized differential transform method to solve the fractional-order multiple chaotic FitzHugh-Nagumo (FHN) neurons model They illustrated the algorithm by studying the dynamics of three coupled chaotic FHN neurons equations with different gap junctions under external electrical stimulation, and the fractional derivatives are described in Discrete Dynamics in Nature and Society the Caputo sense. The aim of this paper is to investigate the dynamical behavior of a discretization fractional order of a modified optically injected semiconductor lasers model.
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