A Conditional Symmetric Memristive System With Infinitely Many Chaotic Attractors

A chaotic system with a hyperbolic function flux-controlled memristor is designed, which exhibits conditional symmetry and attractor growing. The newly introduced cosine function keeps the polarity balance when some of the variables get polarity inversed and correspondingly conditional symmetric coexisting chaotic attractors are coined. Due to the periodicity of the cosine function, the memristive system with infinitely many coexisting attractors shows attractor growing in some special circumstances. Analog circuit experiment proves the theoretical and numerical analysis.

[1]  Chunbiao Li,et al.  A Memristive Chaotic Oscillator With Increasing Amplitude and Frequency , 2018, IEEE Access.

[2]  Qiang Lai,et al.  A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design , 2017, Entropy.

[3]  Huagan Wu,et al.  Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network , 2017 .

[4]  Viet-Thanh Pham,et al.  A Novel Class of Chaotic Flows with Infinite Equilibriums and Their Application in Chaos-Based Communication Design Using DCSK , 2018 .

[5]  Minfang Peng,et al.  Creation and circuit implementation of two‐to‐eight–wing chaotic attractors using a 3D memristor‐based system , 2019, Int. J. Circuit Theory Appl..

[6]  Viet-Thanh Pham,et al.  Autonomous Jerk Oscillator with Cosine Hyperbolic Nonlinearity: Analysis, FPGA Implementation, and Synchronization , 2018, Advances in Mathematical Physics.

[7]  Julien Clinton Sprott,et al.  An infinite 3-D quasiperiodic lattice of chaotic attractors , 2018 .

[8]  Chunhua Wang,et al.  A Novel Multi-Attractor Period Multi-Scroll Chaotic Integrated Circuit Based on CMOS Wide Adjustable CCCII , 2019, IEEE Access.

[9]  Jacques Kengne,et al.  Dynamical analysis of a new multistable chaotic system with hidden attractor: Antimonotonicity, coexisting multiple attractors, and offset boosting , 2019, Physics Letters A.

[10]  Karthikeyan Rajagopal,et al.  Hyperchaotic Memcapacitor Oscillator with Infinite Equilibria and Coexisting Attractors , 2018, Circuits Syst. Signal Process..

[11]  Viet-Thanh Pham,et al.  A chaotic jerk system with non-hyperbolic equilibrium: Dynamics, effect of time delay and circuit realisation , 2018 .

[12]  Ahmad Taher Azar,et al.  Four-wing attractors in a novel chaotic system with hyperbolic sine nonlinearity , 2017 .

[13]  Jacques Kengne,et al.  Antimonotonicity, chaos, quasi-periodicity and coexistence of hidden attractors in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity , 2019, Chaos, Solitons & Fractals.

[14]  Viet-Thanh Pham,et al.  Bistable Hidden Attractors in a Novel Chaotic System with Hyperbolic Sine Equilibrium , 2018, Circuits Syst. Signal Process..

[15]  Bharathwaj Muthuswamy,et al.  Memristor-Based Chaotic Circuits , 2009 .

[16]  I. VagaitsevV.,et al.  Localization of hidden Chua ’ s attractors , 2022 .

[17]  Chunbiao Li,et al.  Constructing Infinitely Many Attractors in a Programmable Chaotic Circuit , 2018, IEEE Access.

[18]  Guanrong Chen,et al.  Conditional symmetry: bond for attractor growing , 2018, Nonlinear Dynamics.

[19]  Julien Clinton Sprott,et al.  Multistability in a Butterfly Flow , 2013, Int. J. Bifurc. Chaos.

[20]  Kehui Sun,et al.  Multivariate Multiscale Complexity Analysis of Self-Reproducing Chaotic Systems , 2018, Entropy.

[21]  Julien Clinton Sprott,et al.  Constructing chaotic systems with conditional symmetry , 2017 .

[22]  Qiang Lai,et al.  Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors , 2018, Chaos, Solitons & Fractals.

[23]  Julien Clinton Sprott,et al.  An infinite 2-D lattice of strange attractors , 2017 .

[24]  Min Fuhong,et al.  Dynamic analysis and circuit implementations of a novel memristive chaotic circuit , 2017, 2017 36th Chinese Control Conference (CCC).

[25]  Julien Clinton Sprott,et al.  Coexisting Hidden Attractors in a 4-D Simplified Lorenz System , 2014, Int. J. Bifurc. Chaos.

[26]  Junkang Ni,et al.  An electronic implementation for Morris–Lecar neuron model , 2016 .

[27]  Qiang Lai,et al.  An Extremely Simple Chaotic System With Infinitely Many Coexisting Attractors , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[28]  Qiang Lai,et al.  Generating Multiple Chaotic Attractors from Sprott B System , 2016, Int. J. Bifurc. Chaos.

[29]  Viet-Thanh Pham,et al.  A new nonlinear oscillator with infinite number of coexisting hidden and self-excited attractors , 2018 .

[30]  Ling Zhou,et al.  A novel no‐equilibrium hyperchaotic multi‐wing system via introducing memristor , 2018, Int. J. Circuit Theory Appl..

[31]  Julien Clinton Sprott,et al.  Multistability in symmetric chaotic systems , 2015 .