In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fracti...In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.展开更多
Dear Editor,Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method(ADM).Dynamics of the fractional-order Lorenz system with derivat...Dear Editor,Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method(ADM).Dynamics of the fractional-order Lorenz system with derivative order and parameter varying is analyzed by means of Lyapunov exponents(LEs),bifurcation diagram.展开更多
Fractional calculus is a 300 years topic,which has been introduced to real physics systems modeling and engineering applications.In the last few decades,fractional-order nonlinear chaotic systems have been widely inve...Fractional calculus is a 300 years topic,which has been introduced to real physics systems modeling and engineering applications.In the last few decades,fractional-order nonlinear chaotic systems have been widely investigated.Firstly,the most used methods to solve fractional-order chaotic systems are reviewed.Characteristics and memory effect in those method are summarized.Then we discuss the memory effect in the fractional-order chaotic systems through the fractionalorder calculus and numerical solution algorithms.It shows that the integer-order derivative has full memory effect,while the fractional-order derivative has nonideal memory effect due to the kernel function.Memory loss and short memory are discussed.Finally,applications of the fractional-order chaotic systems regarding the memory effects are investigated.The work summarized in this manuscript provides reference value for the applied scientists and engineering community of fractional-order nonlinear chaotic systems.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62071496,61901530,and 62061008)the Natural Science Foundation of Hunan Province of China(Grant No.2020JJ5767).
文摘In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.
基金supported by the National Natural Science Foundation of China(62061008,62071496,61901530)。
文摘Dear Editor,Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method(ADM).Dynamics of the fractional-order Lorenz system with derivative order and parameter varying is analyzed by means of Lyapunov exponents(LEs),bifurcation diagram.
基金supported by the Natural Science Foundation of China(Grant Nos.61901530,62071496,and 62061008)the Natural Science Foundation of Hunan Province,China(Grant No.2020JJ5767).
文摘Fractional calculus is a 300 years topic,which has been introduced to real physics systems modeling and engineering applications.In the last few decades,fractional-order nonlinear chaotic systems have been widely investigated.Firstly,the most used methods to solve fractional-order chaotic systems are reviewed.Characteristics and memory effect in those method are summarized.Then we discuss the memory effect in the fractional-order chaotic systems through the fractionalorder calculus and numerical solution algorithms.It shows that the integer-order derivative has full memory effect,while the fractional-order derivative has nonideal memory effect due to the kernel function.Memory loss and short memory are discussed.Finally,applications of the fractional-order chaotic systems regarding the memory effects are investigated.The work summarized in this manuscript provides reference value for the applied scientists and engineering community of fractional-order nonlinear chaotic systems.
