Symmetrical coexisting attractors and extreme multistability induced by memristor operating configurations in SC-CNN

Li, Zhijun; Zhou, Chengyi; Wang, Mengjiao

doi:10.1016/j.aeue.2019.01.013

Cited by 33 publications

(5 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Actually, symmetry of such chaotic system means symmetry of the solutions of system equations, which is the essential reason that coexisting attractors appear in pairs symmetrically (Leutcho et al, 2018). Interestingly, the above phenomenon lies not only in general nonlinear chaotic systems (Chen et al, 2016;Li et al, 2017d;Li and Sprott, 2017b;Leutcho et al, 2018) but also in chaotic systems based on the nonlinear devices of memristor (Peng and Min, 2017;Li et al, 2017a;Wang et al, 2018;Li et al, 2019c), memcapacitor (Yuan et al, 2016) and meminductor (Xu et al, 2017), and even in neural network system (Bao et al, 2019a). For a three-dimensional asymmetric chaotic system with a single attractor, the operation of attractor doubling in three dimensions can produce four pairs of symmetric coexisting attractors, and during this process, the symmetry of the constructed model is an important consideration necessarily (Li et al, 2019a).…”

Section: Mathematical Model and Numerical Simulationsmentioning

confidence: 99%

A chaotic circuit under a new classification framework of inductorless Chua’s circuits

Zhu

Pan

Qiao

2019

View full text Add to dashboard Cite

Purpose This paper aims to classify the inductorless Chua’s circuits into two types from the topological structures and construct a chaotic circuit under this new classification framework. Design/methodology/approach In this paper, two types of inductorless Chua’s circuit models are presented from topological structure, among which the first type of inductorless Chua’s circuit (FTICC) model is much closer to the original Chua’s circuit. Under this classification framework, a new inductorless Chua’s circuit that belongs to the FTICC model is built by replacing LC parallel resonance of the original Chua’s circuit with a second order Sallen–Key band pass filter. Findings Compared with a paradigm of a reported inductorless Chua’s circuit that belongs to the second type of inductorless Chua’s circuit (STICC) model, the newly proposed circuit can present the attractors which are much more closely to the original Chua’s attractors. The dynamical behaviors of coexisting period-doubling bifurcation patterns and boundary crisis are discovered in the newly proposed circuit from both numerical simulations and experimental measurements. Moreover, a crisis scenario is observed that unmixed pairs of symmetric coexisting limit cycles with period-3 traverse through the entire parameter interval between coexisting single-scroll chaotic attractors and double-scroll chaotic attractor. Originality/value The newly constructed circuit enriches the family of inductorless Chua’s circuits, and its simple topology with small printed circuit board size facilitates the various types of engineering applications based on chaos.

show abstract

Section: Mathematical Model and Numerical Simulationsmentioning

confidence: 99%

A chaotic circuit under a new classification framework of inductorless Chua’s circuits

Zhu

Pan

Qiao

2019

View full text Add to dashboard Cite

show abstract

“…A new memristive chaotic system often has one or more equilibrium point sets (one equilibrium point set has infinite equilibrium points), and its dynamic characteristics are sensitive to parameters and strongly depend on the initial values of the memristor. Therefore, memristive chaotic systems are superior to ordinary chaotic systems in terms of dynamic complexity and exist complex dynamic phenomena such as hyperchaos, transient chaos, coexisting attractors, multistability and state transitions [15]. Chaotic signals with complex dynamic characteristics have potential application value in the fields of secure communication, image encryption, and bionics [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Spiking and bursting discharge behaviors in a memristor-based oscillator: analysis and circuit implementation

Song

Shen²,

Zhang³

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

In this study, a voltage-controlled memristor was designed and connected in parallel with an inductor-capacitor to form an oscillator circuit. The memristor, as a natural electronic equivalent for building biological neurons, enabled this oscillator circuit to simulate the four types of firing patterns generated by neurons. By means of a two-parameter scan, a dynamic map of the discharges was created, allowing a more efficient dynamic analysis of the field, and the results were compared with the potassium-sodium ion model of the neuron. The analysis of the stability of the equilibrium point allowed a better understanding of the complex discharge mechanisms generated by the system. The results of the hardware tests and the numerical analysis were in agreement.

show abstract

“…Multistability can be identified through offset-boosting, [19] since multiple coexisting attractors can be visited by changing the offset accordingly. [20,21] For those circuits and systems with memristors, [22][23][24][25][26][27][28] complex chaotic behavior with extreme multistability can also be found. Even in discrete systems, the memristor still gives its nonlinearity for producing chaos.…”

Section: Introductionmentioning

confidence: 99%

A memristive map with coexisting chaos and hyperchaos*

Kong

et al. 2021

Chinese Phys. B

View full text Add to dashboard Cite

By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map, along with which other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points are also captured. The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors. Based on the nonlinear auto-regressive model with exogenous inputs (NARX) for neural network, the dynamics of the memristive map is well predicted, which provides a potential passage in artificial intelligence-based applications.

show abstract

Symmetrical coexisting attractors and extreme multistability induced by memristor operating configurations in SC-CNN

Cited by 33 publications

References 34 publications

A chaotic circuit under a new classification framework of inductorless Chua’s circuits

A chaotic circuit under a new classification framework of inductorless Chua’s circuits

Spiking and bursting discharge behaviors in a memristor-based oscillator: analysis and circuit implementation

A memristive map with coexisting chaos and hyperchaos*

Contact Info

Product

Resources

About