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

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.

Reliable mode-dependent memorized projective lag synchronization for semi-Markovian jumping coupled networks

This article investigates the reliable projective lag synchronization problem for semi-Markovian jumping coupled networks under the master–slave framework. More precisely, a novel mode-dependent memorized synchronization scheme is proposed for the master and slave dynamical networks. By utilizing the Lyapunov-Krasovskii method, sufficient delay-dependent conditions are derived to achieve the reliable synchronization in the mean-square sense. Based on the derived results, the mode-dependent synchronization controller is further designed by convex optimization. In the end, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.