Sliding Mode Matrix-Projective Synchronization for Fractional-Order Neural Networks

Abstract

This work generalizes the projection scaling factor to a general constant matrix and proposes the matrix-projection synchronization (MPS) for fractional-order neural networks (FNNs) based on sliding mode control firstly. This kind of scaling factor is far more complex than the constant scaling factor, and it is highly variable and difficult to predict in the process of realizing the synchronization for the driving and response systems, which can ensure high security and strong confidentiality. Then, the fractional-order integral sliding surface and sliding mode controller for FNNs are designed. Furthermore, the criterion for realizing MPS is proved, and the reachability and stability of the synchronization error system are analyzed, so that the global MPS is realized for FNNs. Finally, a numerical application is given to demonstrate the feasibility of theory analysis. MPS is more general, so it is reduced to antisynchronization, complete synchronization, projective synchronization (PS), and modified PS when selecting different projective matrices. This work will enrich the synchronization theory of FNNs and provide a feasible method to study the MPS of other fractional-order dynamical models.

Adomian Decomposition, Dynamic Analysis and Circuit Implementation of a 5D Fractional-Order Hyperchaotic System

“…System (6) is chaos; the maximum Lyapunov exponent is greater than 0, and the C0 and SE complexity is high, as shown in Figure 5c,d. a ∈ [8,12]. At some points in this interval, the system has three positive Lyapunov exponents, at which time the system complexity reaches the maximum, as shown in Figure 5b-d.…”

“…In addition, the system complexity is also related to the number of positive Lyapunov exponents. From the bifurcation diagram, it can be seen that the system (6) is periodic under parameter a ∈ [5,8), and the maximum Lyapunov exponent of the corresponding system ( 6) is equal to 0. a ∈ [8,12]. System (6) is chaos; the maximum Lyapunov exponent is greater than 0, and the C0 and SE complexity is high, as shown in Figure 5c,d.…”

“…Many scholars have found that the fractional-order model is closer to the actual engineering model than the integer-order calculus model. In the aspect of combining fractional-order systems with nonlinear chaotic systems, many scholars have proposed many fractional-order chaotic systems, such as fractional-order Lorenz chaotic or hyperchaotic systems [5,6], fractional-order chaotic systems with line equilibrium [7], fractional-order entanglement chaotic systems [8], and so on [9][10][11][12][13].…”