Fractional order-induced bifurcations in a delayed neural network with three neurons

Huang, Chengdai; Wang, Huanan; Alsaedi, Ahmed

doi:10.1063/5.0135232

Cited by 13 publications

(2 citation statements)

References 37 publications

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“…For the Riemann-Liouville fractional derivative, its Laplace transform requires the initial values of the fractional derivative terms, which are difficult to calculate in practical applications, and their physical meanings are not yet clear. Nevertheless, the Laplace transform of the Caputo fractional derivative only contains the initial values of the integer derivative terms, which have good physical significance [50]. In view of this, the Caputo fractional derivative is employed to handle the model in this paper, which can be described as…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

Tang,

Li,

Huang

2024

Phys. Scr.

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A novel 4D fractional-order chaotic entanglement system based on sinusoidal functions is established in this paper. We aim to reveal the relationship between the dynamical behavior of the new system and its entanglement coefficients. It is found that the equilibrium point of the system varies regularly with the successive change of the entanglement coefficient. The supercritical pitchfork bifurcation phenomenon of the new system is discussed based on the fractional-order stability theory. Furthermore, sufficient conditions and threshold for supercritical Hopf bifurcation caused by the entanglement coefficient are provided. Finally, the route to chaos of the new system is explored utilizing multiple numerical indicators, such as spectral entropy complexity, bifurcation diagrams, Lyapunov exponential spectrum, phase portraits, and 0-1 test curves. The results indicate that in addition to various chaotic attractors, there are phenomena such as period-doubling bifurcations, period windows, and coexisting symmetric attractors (periodic or chaotic).

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Section: Mathematical Preliminariesmentioning

confidence: 99%

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

Tang,

Li,

Huang

2024

Phys. Scr.

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“…This versatility and power of fractional calculus contribute significantly to enhancing our understanding and modeling of real-world systems [1,2]. Fractional calculus is widely used in many fields, including complex system modeling [3,4], signal processing [5], diffusion processes [6], viscoelastic materials [7], etc.…”

Section: Introductionmentioning

confidence: 99%

Fast Dynamical Analysis of High-dimensional Fractional-Order Memristive-Coupled Hopffeld Neural Networks utilizing a modiffed Non-Classical Methods

Liu,

Chen,

Liu

2023

Preprint

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Solving high-dimensional fractional differential equations has consistently remained one of the most signiffcant challenges within the realm of fractional calculus. Classical numerical methods often grapple with extensive history datasets, resulting in decreased computational efffciency. Existing non-classical methods frequently result in huge dimensional integer-order systems. To address these issues, an improved non-classical method is established in this paper. By introducing an integral interval decomposition strategy, the decay rate of the integrand in the non-classical method is signiffcantly accelerated, achieving a transition from algebraic decay to exponential decay. Consequently, there is a substantial reduction in the dimensionality of the approximate integerorder systems. Simultaneously, the introduction of the interpolation quadrature method further improves the computational accuracy. Theoretical analysis and numerical examples demonstrate that the proposed method offers substantial performance advantages in tackling fractional differential equations. In conclusion, the dynamic behavior of a high-dimensional memristive-coupled Hopffeld neural network was effectively investigated using the proposed method by phase diagrams and bifurcation diagrams. The proposed method demonstrates the capability to accurately identify both chaotic and periodic behavior within the system. Furthermore, it offers a substantial reduction in computation time for high-dimensional systems. This efffciency in capturing complex dynamics while decreasing computational overhead can be highly advantageous in various applications. It holds crucial theoretical implications for the numerical solution of fractional differential equation. Furthermore, it has the potential to foster and stimulate research and practical applications within the realm of fractional order systems.

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Chaos and firing patterns in a discrete fractional Hopfield neural network model

He,

Vignesh,

Rondoni

et al. 2023

Nonlinear Dyn

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Fractional order-induced bifurcations in a delayed neural network with three neurons

Cited by 13 publications

References 37 publications

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

A novel entanglement functions-based 4D fractional-order chaotic system and its bifurcation analysis

Fast Dynamical Analysis of High-dimensional Fractional-Order Memristive-Coupled Hopffeld Neural Networks utilizing a modiffed Non-Classical Methods

Chaos and firing patterns in a discrete fractional Hopfield neural network model

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