Extreme Multistability of a Fractional-Order Discrete-Time Neural Network

Almatroud, A. Othman

doi:10.3390/fractalfract5040202

Cited by 13 publications

(5 citation statements)

References 22 publications

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“…In order to have a deeper understanding of neuronal networks, researchers in various fields have explored the characteristics and dynamical behavior of neuron models from the perspective of different mathematical functions and analyses. [1][2][3][4][5][6][7][8][9][10] Memristors are the fourth basic passive circuit element after resistors, inductors and capacitors. It can be seen from Ref.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behaviors in discrete memristor-coupled small-world neuronal networks

Lu 鲁,

Xie 谢,

Lu 卢

et al. 2024

Chinese Phys. B

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Brain is a complex network system in which a large number of neurons are widely connected to each other and transmit signals to each other. The memory characteristic of memristors makes them suitable for simulating neuronal synapses with plasticity. In this paper, a memristor is used to simulate synapse, and a discrete small-world neuronal network is constructed based on Rulkov neurons and its dynamical behavior is explored. We explore the influence of system parameter on the dynamical behaviors of the discrete small-world network, and the system shows a variety of firing patterns such as spiking firing and triangular bursting firing when the neuronal parameter α is changed. The numerical simulation results based on Matlab show that the network topology can affect the synchronous firing behavior of the neuronal network, and the higher the reconnection probability, the number of nearest neurons, and the more significant the synchronization state of neurons. In addition, by increasing the coupling strength of memristor synapses, synchronization performance is promoted. The results of this paper can boost the research process of complex neuronal networks coupled with memristor synapse and further promote the development of neuroscience.

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Section: Introductionmentioning

confidence: 99%

Dynamical behaviors in discrete memristor-coupled small-world neuronal networks

Lu 鲁,

Xie 谢,

Lu 卢

et al. 2024

Chinese Phys. B

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“…Gasri et al [27] revealed the rich chaotic dynamics of a novel fractional-order map with infinite line of equilibrium points, while In [28], Khennaoui et al have investigated the chaotic dynamics of a new 2D discrete system without equilibrium points. Furthermore, multistability in fractional discrete chaotic maps has recently received a lot of attention [29][30][31][32][33]. Generally, multistability is a phenomenon that may occur in nonlinear dynamical systems and denotes the existence of many forms of attractors in response to a variety of initial conditions and system characteristics.…”

Section: Introductionmentioning

confidence: 99%

Hidden multistability of fractional discrete non-equilibrium point memristor based map

et al. 2023

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At present, the multistability analysis in discrete nonlinear fractional-order systems is a subject that is receiving a lot of attention. In this article, a new discrete non-equilibrium point memristor-based map with $\gamma-th$ Caputo fractional difference is introduced. In addition, in the context of the commensurate and non-commensurate instances, the non-linear dynamics of the suggested discrete fractional map, such as its multistability, hidden chaotic attractor, and hidden hyperchaotic attractor, are investigated through several numerical techniques, including Lyapunov exponents, phase attractors, bifurcation diagrams, and the $0–1$ test. This dynamic behaviors suggests that the fractional discrete memristive map has a hidden multistability. Finally, to validate the presence of chaos, a complexity analysis is carried out using approximation entropy ($ApEn$) and the $C_0$ measure. The findings show that the model has a high degree of complexity, which is affected by the system parameters and the fractional values.

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“…Various types of dynamics for multistability in an M-dimensional hyperchaotic map [24], bistability in a model of periodically forced system [25], a memristive hyperchaotic discrete system with multistability [26], and a new method to design extreme multistable maps [27] are some research in this area. In addition, extreme multistability in a fractional-order discrete network in [28] and the multistability of a 2D discrete system with a sine term have been studied in [29].…”

Section: Introductionmentioning

confidence: 99%

A novel chaotic map with a shifting parameter and stair-like bifurcation diagram: dynamical analysis and multistability

Ramadoss¹,

Natiq²,

Nazarimehr

et al. 2023

Phys. Scr.

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In this paper, the behavior of a 1D chaotic map is proposed which includes two sine terms and shows unique dynamics. By varying the bifurcation parameter, the map has a shift, and the system's dynamics are generated around the cross points of the map and the identity line. The irrational frequency of the sine term makes the system have stable fixed points in some parameter intervals by increasing the bifurcation parameter. So, the bifurcation diagram of the system shows that the trend of the system's dynamics changes in a stair shape with slope one by changing the bifurcation parameter. Due to the achieving multiple steady states in some intervals of the parameter, the proposed system is known as multistable. The multistability dynamics of the map are investigated with the help of cobweb diagrams which reveal an interesting asymmetry in repeating parts of the bifurcation diagram.

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Extreme Multistability of a Fractional-Order Discrete-Time Neural Network

Cited by 13 publications

References 22 publications

Dynamical behaviors in discrete memristor-coupled small-world neuronal networks

Dynamical behaviors in discrete memristor-coupled small-world neuronal networks

Hidden multistability of fractional discrete non-equilibrium point memristor based map

A novel chaotic map with a shifting parameter and stair-like bifurcation diagram: dynamical analysis and multistability

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