Coexistence of periodic and strange attractor in a memristive band pass filter circuit with amplitude control

By replacing the cubic voltage-controlled memristor emulator with the quadratic one in an existing memristive band pass filter (BPF) chaotic circuit, a modified memristive BPF circuit with two asymmetric equilibria is proposed. A dimensionless model is used to analyse the fundamental properties. The nonlinear techniques including phase portraits, bifurcation diagrams, Lyapunov exponents, Poincare sections, and attraction basins are used to analyse the complex dynamics. The striking feature is that this system exhibits the bi-stability phenomenon of coexisting periodic and strange attractors with adjustable amplitudes. The results of theoretical analysis are effectively verified by numerical simulations and hardware experiments.

[1]  Bocheng Bao,et al.  Hidden Bursting Firings and Bifurcation Mechanisms in Memristive Neuron Model With Threshold Electromagnetic Induction , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Guangyi Wang,et al.  Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria , 2018, Commun. Nonlinear Sci. Numer. Simul..

[3]  L. Chua.  Memristor-The missing circuit element , 1971 .

[4]  Jacques Kengne,et al.  Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit , 2016 .

[5]  Viet-Thanh Pham,et al.  A hyperchaotic memristor oscillator with fuzzy based chaos control and LQR based chaos synchronization , 2018, AEU - International Journal of Electronics and Communications.

[6]  Viet-Thanh Pham,et al.  A Modified Multistable Chaotic Oscillator , 2018, Int. J. Bifurc. Chaos.

[7]  Huagan Wu,et al.  Complex transient dynamics in periodically forced memristive Chua’s circuit , 2015 .

[8]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[9]  Julien Clinton Sprott,et al.  Detecting Hidden Chaotic Regions and Complex Dynamics in the Self-Exciting Homopolar Disc Dynamo , 2017, Int. J. Bifurc. Chaos.

[10]  Karthikeyan Rajagopal,et al.  Bifurcation and chaos in time delayed fractional order chaotic memfractor oscillator and its sliding mode synchronization with uncertainties , 2017 .

[11]  Bocheng Bao,et al.  Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit , 2016 .

[12]  S. Jafari,et al.  A chaotic memcapacitor oscillator with two unstable equilibriums and its fractional form with engineering applications , 2018 .

[13]  Julien Clinton Sprott,et al.  Amplitude control approach for chaotic signals , 2013 .

[14]  Viet-Thanh Pham,et al.  Bifurcation analysis and circuit realization for multiple-delayed Wang–Chen system with hidden chaotic attractors , 2016 .

[15]  M. Yao,et al.  Study of hidden attractors, multiple limit cycles from Hopf bifurcation and boundedness of motion in the generalized hyperchaotic Rabinovich system , 2015 .

[16]  Jun Tang,et al.  A review for dynamics in neuron and neuronal network , 2017, Nonlinear Dynamics.

[17]  Christos Volos,et al.  A novel memristive neural network with hidden attractors and its circuitry implementation , 2015, Science China Technological Sciences.

[18]  Yihua Hu,et al.  Flux–Charge Analysis of Two-Memristor-Based Chua's Circuit: Dimensionality Decreasing Model for Detecting Extreme Multistability , 2020, IEEE Transactions on Industrial Electronics.

[19]  K. Rajagopal,et al.  A hyperchaotic memristor system with exponential and discontinuous memductance function , 2018, AEU - International Journal of Electronics and Communications.

[20]  Huagan Wu,et al.  Controlling extreme multistability of memristor emulator-based dynamical circuit in flux–charge domain , 2018 .

[21]  Qingdu Li,et al.  On hyperchaos in a small memristive neural network , 2014 .

[22]  Wei Zhang,et al.  Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo. , 2017, Chaos.

[23]  Mo Chen,et al.  Coexisting Behaviors of Asymmetric Attractors in Hyperbolic-Type Memristor based Hopfield Neural Network , 2017, Front. Comput. Neurosci..

[24]  Julien Clinton Sprott,et al.  Constructing Chaotic Systems with Total Amplitude Control , 2015, Int. J. Bifurc. Chaos.

[25]  Karthikeyan Rajagopal,et al.  FPGA implementation of fractional-order discrete memristor chaotic system and its commensurate and incommensurate synchronisations , 2017 .

[26]  Huagan Wu,et al.  A Simple Third-Order Memristive Band Pass Filter Chaotic Circuit , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[27]  Bocheng Bao,et al.  Two-memristor-based Chua’s hyperchaotic circuit with plane equilibrium and its extreme multistability , 2017 .

[28]  Sundarapandian Vaidyanathan,et al.  A novel memristive time–delay chaotic system without equilibrium points , 2016 .

[29]  Julien Clinton Sprott,et al.  Crisis in Amplitude Control Hides in Multistability , 2016, Int. J. Bifurc. Chaos.

[30]  Bocheng Bao,et al.  Extreme multistability in a memristive circuit , 2016 .

[31]  Guanrong Chen,et al.  A chaotic system with only one stable equilibrium , 2011, 1101.4067.

[32]  Yihua Hu,et al.  Bi-Stability Phenomenon in Constant On-Time Controlled Buck Converter With Small Output Capacitor ESR , 2018, IEEE Access.

[33]  Sundarapandian Vaidyanathan,et al.  Hidden attractors in a chaotic system with an exponential nonlinear term , 2015 .

[34]  Julien Clinton Sprott,et al.  Simple Chaotic Flows with a Curve of Equilibria , 2016, Int. J. Bifurc. Chaos.

[35]  Viet-Thanh Pham,et al.  A flexible chaotic system with adjustable amplitude, largest Lyapunov exponent, and local Kaplan–Yorke dimension and its usage in engineering applications , 2018 .

[36]  Jacques Kengne,et al.  Coexisting bifurcations in a memristive hyperchaotic oscillator , 2018, AEU - International Journal of Electronics and Communications.

[37]  Bocheng Bao,et al.  Hidden extreme multistability in memristive hyperchaotic system , 2017 .

[38]  Julien Clinton Sprott,et al.  A Simple Chaotic Flow with a Plane of Equilibria , 2016, Int. J. Bifurc. Chaos.