Realizing stochastic fixed-time synchronization between two nonlinear chaotic finance systems

Abstract

The issue of stochastic fixed-time synchronization (SFxS) between two nonlinear chaotic finance systems (CFSs) in noisy environment is addressed by this investigation. Two novel strategies, including the adaptive and fixed-time control, are integrated organically, which steers the CFSs to realize synchronization within a fixed-time, and meanwhile the controlling gains can be updated by the designed adaptive law. Particularly, the designed adaptive fixed-time controlling (AFC) scheme is differentiable, so that the chattering phenomenon can be alleviated and even eliminated effectively. Furthermore, by the stochastic Lyapunov stability analysis, the sufficient criterion is derived for realizing the SFxS of CFSs, and the upper-bound expectation of settling-time (UET) is estimated as well. At last, the numerical experiments are arranged to verify the correctness and feasibility of analytical results, the influence of noisy perturbation on the convergence rate is uncovered, and the interesting similar Dragon–King events are observed.

Predefined-time stabilization of Lorenz system with applications for stabilizing and synchronizing chaotic finance systems

“…In terms of fractional-order CFSs, the fixed-time synchronization problem has been also discussed recently [40]. Moreover, the terminal sliding mode control [41] has been adopted and the influence of stochastic noise [42,43] has been considered for reaching the fixedtime stabilization/synchronization of CFSs. Similar to the fixed-time convergence for Lorenz systems, the estimation of UbCT in the efforts of [30], [39][40][41][42][43] is very complicated, which also relates with the system dimension and controlling parameters.…”

“…Moreover, the terminal sliding mode control [41] has been adopted and the influence of stochastic noise [42,43] has been considered for reaching the fixedtime stabilization/synchronization of CFSs. Similar to the fixed-time convergence for Lorenz systems, the estimation of UbCT in the efforts of [30], [39][40][41][42][43] is very complicated, which also relates with the system dimension and controlling parameters. Therefore, the topic that how to achieve fast synchronization of CFSs with an explicit UbCT is interesting and not resolved at the moment.…”