Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons

Chen, Chengjie; Chen, Jingqi; Bao, Han; Chen, Mo; Bao, Bocheng

doi:10.1007/s11071-019-04762-8

Cited by 201 publications

(63 citation statements)

References 46 publications

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“…Compared with chaos, hyperchaos possesses more randomness, complex dynamical behavior, and unpredictability with at least two positive Lyapunov exponents (LEs). Numerous examples of novel hyperchaotic systems [4][5][6][7][8][9] can be intensively discovered, and they have been widely applied in many fields, such as cryptography [10], neural network [11], synchronization [12,13], and secure communications [14,15]. e memristor that had been postulated as the fourth basic circuit element in 1971 by Chua [16] is a two-terminal passive electronic element described by nonlinear constitutive relation of charge q and flux φ and was for the first time fabricated in 2008 by Williams's group of HP Labs [17].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis and Circuit Realization of a Novel No-Equilibrium 5D Memristive Hyperchaotic System with Hidden Extreme Multistability

Wan

Zhou

et al. 2020

Complexity

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In this paper, a novel no-equilibrium 5D memristive hyperchaotic system is proposed, which is achieved by introducing an ideal flux-controlled memristor model and two constant terms into an improved 4D self-excited hyperchaotic system. The system parameters-dependent and memristor initial conditions-dependent dynamical characteristics of the proposed memristive hyperchaotic system are investigated in terms of phase portrait, Lyapunov exponent spectrum, bifurcation diagram, Poincaré map, and time series. Then, the hidden dynamic attractors such as periodic, quasiperiodic, chaotic, and hyperchaotic attractors are found under the variation of its system parameters. Meanwhile, the most striking phenomena of hidden extreme multistability, transient hyperchaotic behavior, and offset boosting control are revealed for appropriate sets of the memristor and other initial conditions. Finally, a hardware electronic circuit is designed, and the experimental results are well consistent with the numerical simulations, which demonstrate the feasibility of this novel 5D memristive hyperchaotic system.

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Section: Introductionmentioning

confidence: 99%

Dynamic Analysis and Circuit Realization of a Novel No-Equilibrium 5D Memristive Hyperchaotic System with Hidden Extreme Multistability

Wan

Zhou

et al. 2020

Complexity

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“…The coexistence of self-excited attractors or hidden attractors has been found in various kinds of continuous ordinary differential systems. These ordinary differential systems contain the purely mathematical chaotic and hyperchaotic systems [ 8 , 9 ], memristor-based chaotic circuits and systems [ 10 , 11 ], and Hopfield neural networks [ 12 , 13 ]. When the coexisting attractors reach an infinite number, this phenomenon is defined as extreme multistability [ 14 ], which has been reported in many memristor-based chaotic systems [ 15 , 16 ].…”

Section: Introductionmentioning

confidence: 99%

Coexisting Infinite Orbits in an Area-Preserving Lozi Map

Chen

et al. 2020

Entropy

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Extreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map under specific parameter settings. We use the bifurcation diagram and phase orbit diagram to disclose the coexisting infinite orbits that include period, quasi-period and chaos with different types and topologies, and we employ the spectral entropy and sample entropy to depict the initial values-related complexity. Finally, a microprocessor-based hardware platform is developed to acquire four sets of four-channel voltage sequences by switching the initial values. The results show that the area-preserving Lozi map displays coexisting infinite orbits with complicated complexity distributions, which heavily rely on its initial values.

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“…With the advent of memristors, many types of artificial neural networks have been improved by memristors, such as Cellular neural network (CNN) and Hopfield neural network (HNN) [9][10][11][12][13][14][15][16][17][18][19][20]. The research on CNN mainly lies in its application [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Hidden Multistability in a Memristor-Based Cellular Neural Network

Lin

Wang

2020

Advances in Mathematical Physics

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In this paper, we report a novel memristor-based cellular neural network (CNN) without equilibrium points. Dynamical behaviors of the memristor-based CNN are investigated by simulation analysis. The results indicate that the system owns complicated nonlinear phenomena, such as hidden attractors, coexisting attractors, and initial boosting behaviors of position and amplitude. Furthermore, both heterogeneous multistability and homogenous multistability are found in the CNN. Finally, Multisim circuit simulations are performed to prove the chaotic characteristics and multistability of the system.

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Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons

Cited by 201 publications

References 46 publications

Dynamic Analysis and Circuit Realization of a Novel No-Equilibrium 5D Memristive Hyperchaotic System with Hidden Extreme Multistability

Dynamic Analysis and Circuit Realization of a Novel No-Equilibrium 5D Memristive Hyperchaotic System with Hidden Extreme Multistability

Coexisting Infinite Orbits in an Area-Preserving Lozi Map

Hidden Multistability in a Memristor-Based Cellular Neural Network

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