Synchronization between fractional-order Ravinovich–Fabrikant and Lotka–Volterra systems

Unusual dynamics and hidden attractors of the Rabinovich–Fabrikant system

“…In fact, the interest in this system is continuously increasing (see e.g. [3,4,5,6,7,8,9,10]). The mathematical RF model is defined by the following system of ODEs:…”

Dynamical Behavior Analysis and Control of a Fractional-order Discretized Tumor Model

“…There are many schemes to achieve chaos control, such as linear and nonlinear feedback control and active control etc. [10,11]. In this paper, linear feedback control method is used to control chaos.…”

Projective synchronization between different fractional-order hyperchaotic systems with uncertain parameters using proposed modified adaptive projective synchronization technique

“…In recent years, various type of synchronization scheme such as linear and nonlinear feedback synchronization , back stepping control , active control , adaptive control , sliding mode control , projective synchronization , and function projective synchronization have been successfully applied to chaos synchronization. In 1999, Mainieri and Rehacek for the first time present the projective synchronization method, which is one of the most noticeable one because it can obtain faster communication with its proportional feature .…”

“…Thus, it appears to be structurally stable. These ideas have motivated the authors to construct a real mathematical model for synchronization of two different fractional-orders chaotic systems.The pioneering work of Pecore and Corrall [1] introduced a method about synchronization between identical or nonidentical system with different initial conditions, which has attracted a great deal of interest in various fields due to its important applications in ecological systems [2], physical systems [3], chemical systems [4], modeling brain activity, system identification, pattern recognition phenomena, and secure communications [5,6].In recent years, various type of synchronization scheme such as linear and nonlinear feedback synchronization [7-9], back stepping control [10] , active control [11][12][13], adaptive control [14][15][16][17][18][19][20][21], sliding mode control [22,23], projective synchronization [24,25], and function projective synchronization [26,27] have been successfully applied to chaos synchronization. In 1999, Mainieri and Rehacek [28] for the first time present the projective synchronization method, which is one of the most noticeable one because it can obtain faster communication with its proportional feature [29,30].…”