On hyperchaos in a small memristive neural network

Li, Qingdu; Song, Tianming; Zeng, Hongzheng; Zhou, Tingting

doi:10.1007/s11071-014-1498-7

Cited by 100 publications

(23 citation statements)

References 39 publications

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“…By applying Lyapunov stability theory, we will prove that the master system (15) and the slave system (16) are synchronized when using the adaptive control (19).…”

Section: Synchronization Of the Identical Systems With Infinite Equilmentioning

confidence: 99%

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A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

Pham

Volos

Vaidyanathan

et al. 2016

Advances in Mathematical Physics

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Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system's chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.

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“…By applying Lyapunov stability theory, we will prove that the master system (15) and the slave system (16) are synchronized when using the adaptive control (19).…”

Section: Synchronization Of the Identical Systems With Infinite Equilmentioning

confidence: 99%

“…A new class of chaotic systems with circle and square equilibrium was discovered by using predefined general forms [12,13]. In addition, hyperchaotic behavior was observed in a four-dimensional system with a curve of equilibria [14] or four-dimensional systems with a line of equilibria [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

Pham

Volos

Vaidyanathan

et al. 2016

Advances in Mathematical Physics

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“…In comparison with the known memristive systems [17][18][19][20][21], the new constructed system has a number of special characteristics. Almost all the reported memristive systems are the systems with single-wing or two-wing attractors [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium

et al. 2015

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A new hyper-chaotic system is presented in this paper by adding a smooth flux-controlled memristor and a cross-product item into a three-dimensional autonomous chaotic system. It is exciting that this new memristive system can show a four-wing hyperchaotic attractor with a line equilibrium. The dynamical behaviors of the proposed system are analyzed by Lyapunov exponents, bifurcation diagram and Poincaré maps. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of hyperchaos in the system is verified theoretically. Finally, an electronic circuit is designed to implement the hyperchaotic memristive system.

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“…The memristor is known as the fourth fundamental electronic element, which is originally predicted by Chua in 1971 [25,26] and firstly invented by Williams et al [27] at HP in 2008. Due to its non-volatility, nano-size, low power consumption, etc., the memristor has many promising applications in electronics, especially for artificial synapses of neural networks [24,28,29]; therefore, it is significant to study the complex dynamics of the memristive systems with infinitely many equilibria [30].…”

Section: Introductionmentioning

confidence: 99%

Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria

Zeng

2014

Nonlinear Dyn

Self Cite

166

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This paper studies a four-dimensional (4D) memristive system modified from the 3D chaotic system proposed by Lü and Chen. The new system keeps the symmetry and dissipativity of the original system and has an uncountable infinite number of stable and unstable equilibria. By varying the strength of the memristor, we find rich complex dynamics, such as limit cycles, torus, chaos, and hyperchaos, which can peacefully coexist with the stable equilibria. To explain such coexistence, we compute the unstable manifolds of the equilibria, find that the manifolds create a safe zone for the hyperchaotic attractor, and also find many heteroclinic orbits. To verify the existence of hyperchaos in the 4D memristive circuit, we carry out a computerassisted proof via a topological horseshoe with twodirectional expansions, as well as a circuit experiment on oscilloscope views.

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On hyperchaos in a small memristive neural network

Cited by 100 publications

References 39 publications

A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium

Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria

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