This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems.In particular,both Caputo definition and Riemann-Liouville definition are under consideration.With...This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems.In particular,both Caputo definition and Riemann-Liouville definition are under consideration.With the convex assumption,several elementary fractional difference inequalities on Lyapunov functions are developed.According to the essential features of nabla fractional calculus,the sufficient conditions are given first to guarantee the asymptotic stability for the incommensurate system by using the direct Lyapunov method.To substantiate the efficacy and effectiveness of the theoretical results,four examples are elaborated.展开更多
The aim of this paper is to study complex modified projective synchronization（CMPS） between fractional-order chaotic nonlinear systems with incommensurate orders. Based on the stability theory of incommensurate frac...The aim of this paper is to study complex modified projective synchronization（CMPS） between fractional-order chaotic nonlinear systems with incommensurate orders. Based on the stability theory of incommensurate fractional-order systems and active control method, control laws are derived to achieve CMPS in three situations including fractional-order complex Lorenz system driving fractional-order complex Chen system, fractional-order real Rssler system driving fractional-order complex Chen system, and fractionalorder complex Lorenz system driving fractional-order real Lü system. Numerical simulations confirm the validity and feasibility of the analytical method.展开更多
We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability t...We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory, the fractional order differential inequality, and the adaptive strategy. This synchronization approach is simple, universal, and theoretically rigorous. It enables the synchronization of O fractional-order chaotic systems to be achieved in a systematic way. The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.62273092the Science Climbing Project under Grant No.4307012166+3 种基金the Anhui Provincial Natural Science Foundation under Grant No.1708085QF141the Fundamental Research Funds for the Central Universities under Grant No.WK2100100028the General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2016M602032the fund of China Scholarship Council under Grant No.201806345002。
文摘This paper investigates the problem of stability analysis for a class of incommensurate nabla fractional order systems.In particular,both Caputo definition and Riemann-Liouville definition are under consideration.With the convex assumption,several elementary fractional difference inequalities on Lyapunov functions are developed.According to the essential features of nabla fractional calculus,the sufficient conditions are given first to guarantee the asymptotic stability for the incommensurate system by using the direct Lyapunov method.To substantiate the efficacy and effectiveness of the theoretical results,four examples are elaborated.
基金supported by Key Program of National Natural Science Foundation of China (No. 61533011)National Natural Science Foundation of China (Nos. 61273088 and 61603203)
文摘The aim of this paper is to study complex modified projective synchronization（CMPS） between fractional-order chaotic nonlinear systems with incommensurate orders. Based on the stability theory of incommensurate fractional-order systems and active control method, control laws are derived to achieve CMPS in three situations including fractional-order complex Lorenz system driving fractional-order complex Chen system, fractional-order real Rssler system driving fractional-order complex Chen system, and fractionalorder complex Lorenz system driving fractional-order real Lü system. Numerical simulations confirm the validity and feasibility of the analytical method.
基金Project supported by the Natural Science Foundation of Hebei Province, China （Grant No. A2010000343）.
文摘We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory, the fractional order differential inequality, and the adaptive strategy. This synchronization approach is simple, universal, and theoretically rigorous. It enables the synchronization of O fractional-order chaotic systems to be achieved in a systematic way. The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.
