Studying Stochastic Resonance Phenomenon in the Fractional-Order Lorenz-Like Chaotic System

At present, stochastic resonance (SR) based on Duffing and Langevin equations has been widely studied, but there is little research on SR phenomenon in higher-dimensional fractional-order systems. Based on the fractional-order Lorenz-like system, the SR phenomenon is studied from the perspective of equilibrium point in this paper. The dynamic process of SR phenomenon is presented, and several key parameters are derived. The results of numerical simulation show that the boundary of SR and chaos system will be broken if the order of the fractional-order system or internal parameters is properly adjusted, and the effect of SR phenomenon will also be influenced. This paper connects two important nonlinear phenomena (chaos and SR) based on the fractional-order system, which provides a new idea for the conversion between chaos and SR systems.

[1]  Yulin Jin,et al.  An adaptive fractional stochastic resonance method based on weighted correctional signal-to-noise ratio and its application in fault feature enhancement of wind turbine. , 2021, ISA transactions.

[2]  C. J. Zúñiga-Aguilar,et al.  Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks , 2021, Engineering with Computers.

[3]  Behzad Ghanbari,et al.  Two efficient numerical schemes for simulating dynamical systems and capturing chaotic behaviors with Mittag–Leffler memory , 2020, Engineering with Computers.

[4]  J. Redwing,et al.  Stochastic resonance in MoS2 photodetector , 2020, Nature Communications.

[5]  Feifei Yang,et al.  Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application , 2020 .

[6]  Jiao Shangbin,et al.  Research on detection method of multi-frequency weak signal based on stochastic resonance and chaos characteristics of Duffing system , 2020 .

[7]  Derek Abbott,et al.  Stochastic resonance in Hopfield neural networks for transmitting binary signals , 2020 .

[8]  Zhixing Li,et al.  A multi-parameter constrained potential underdamped stochastic resonance method and its application for weak fault diagnosis , 2019, Journal of Sound and Vibration.

[9]  Peiguo Liu,et al.  State observer for stochastic resonance in bistable system , 2019, Physics Letters A.

[10]  Yan Huang,et al.  A parameter-adaptive stochastic resonance based on whale optimization algorithm for weak signal detection for rotating machinery , 2019, Measurement.

[11]  D. Bozovic,et al.  Noise-induced chaos and signal detection by the nonisochronous Hopf oscillator. , 2019, Chaos.

[12]  P. Hänggi,et al.  Quantum stochastic resonance in an a.c.-driven single-electron quantum dot , 2019, Nature Physics.

[13]  Jimeng Li,et al.  A novel adaptive stochastic resonance method based on coupled bistable systems and its application in rolling bearing fault diagnosis , 2019, Mechanical Systems and Signal Processing.

[14]  Yi Lu,et al.  Fractional stochastic resonance multi-parameter adaptive optimization algorithm based on genetic algorithm , 2018, Neural Computing and Applications.

[15]  R. Schniepp,et al.  Stochastic resonance in the human vestibular system – Noise-induced facilitation of vestibulospinal reflexes , 2017, Brain Stimulation.

[16]  Joaquín J. Torres,et al.  Inverse stochastic resonance in networks of spiking neurons , 2017, PLoS Comput. Biol..

[17]  Miguel A. F. Sanjuán,et al.  Detecting the weak high-frequency character signal by vibrational resonance in the Duffing oscillator , 2017 .

[18]  G. Parisi,et al.  A Theory of Stochastic Resonance in Climatic Change , 1983 .

[19]  G. Parisi,et al.  Stochastic resonance in climatic change , 1982 .

[20]  Jiaxu Wang,et al.  Weak feature enhancement in machinery fault diagnosis using empirical wavelet transform and an improved adaptive bistable stochastic resonance. , 2019, ISA transactions.