A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

Abstract

Projective-lag synchronization of complex systems has attracted much attention in the past two decades. However, the majority of previous studies concentrated on continuous-time chaotic systems or discrete-time chaotic systems with the same dimensions. In our present study, a general method for projective-lag synchronization of different discrete-time chaotic systems characterized with different dimensions is first demonstrated. On the basis of stability theory of discrete-time dynamical systems and Lyapunov stability theory, general controllers are designed by using the active control method. The method could achieve projective-lag synchronization in both cases: [Formula: see text] and [Formula: see text]. The effectiveness and feasibility of the proposed method is demonstrated by the projective-lag synchronization between two-dimensional Lorenz discrete-time system and three-dimensional Stefanski map, as well as between the three-dimensional generalized Hénon map and the two-dimensional quadratic map, respectively.

Global asymptotic stability and projective lag synchronization for uncertain inertial competitive neural networks

“…The combination of projective synchronization and lag synchronization can better improve the signal transmission and application value. At present, Feng et al [47] studied a general method for projective lag synchronization of heterogeneous chaotic maps with different dimensions. Pratap et al [48] discussed global projection lag synchronization of mixed time-varying delay BAM NN with fractional memristors.…”

Observer-based adaptive neural network control design for projective synchronization of uncertain chaotic systems

“…Pecora and Carroll were the first to discover the phenomena of chaotic synchronization (Pecora and Carroll, 1990). After that, various types of chaos synchronization have been suggested in the literature for over two decades, such as complete synchronization (Korneev et al, 2021), phase synchronization (Mao et al, 2021), lag synchronization (Mihana et al, 2020), anti-synchronization (Yu et al, 2020), impulsive synchronization (Ao et al, 2020), exponential synchronization (Xu et al, 2020), projective synchronization (Boubellouta and Boulkroune, 2019), projective-lag synchronization (Feng et al, 2021), and so on (Eroglu et al, 2017; Zouari et al, 2017). The projective synchronization technique which consists in synchronizing the dynamical states of a master-slave system with a scaling factor is one of the most popular methods for synchronization (Ren and Zhang, 2019).…”

Global asymptotic stability and projective lag synchronization for uncertain inertial competitive neural networks

“…The combination of projective synchronization and lag synchronization can better improve the signal transmission and application value. At present, Feng and Yang [47] had studied a general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions. Pratap and Cao [48]et al…”