On Variable-Order Fractional Discrete Neural Networks: Existence, Uniqueness and Stability

Almatroud, Othman Abdullah; Hioual, Amel; Ouannas, Adel; Sawalha, Mohammed Mossa; Alshammari, Saleh; Alshammari, Mohammad

doi:10.3390/fractalfract7020118

Cited by 14 publications

(3 citation statements)

References 31 publications

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“…[11] that memristors have unique nonlinearity and memory characteristics, and researchers have constructed different new chaotic systems based on discrete memristor models. [12][13][14][15][16][17][18][19][20] Neuronal networks are able to generate complex dynamical behavior when memristors are applied to the field of neuronal networks, which is beneficial for simulating real biological neuronal networks. A three-order neuron circuit with complex neuromorphic behavior was established by inserting a current-controlled Chua Corsage memristor into a resonator.…”

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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“…Almeida et al [24] provide numerical schemes to deal with variable-order fractional differential equations. The variable order fractional differential equation is a powerful tool that contributes to artificial intelligence; Wang et al [25] proposed a fractional order neural network, and Almatroud et al [26] discussed the existence and uniqueness of variable order neural networks.…”

Section: Introductionmentioning

confidence: 99%

Optimizing Nonlinear Variable Fractional Volta’s System Design with RBFNN-Enhanced Intelligence Computing Networks

Malik,

Bashir,

Akhtar

et al. 2024

Preprint

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The study of variable order differential operators has emerged as a powerful tool for effectively modeling nonlinear fractional differential equations and chaotic systems. In this research, we employ a nonlinear, flexible structure of radial basis function neural network (RBFNN) to model the convective flow of the generalized nonlinear Volta's system in the variable order fractional domain. The intricate physical parameters of the fractional-order system are first computed using a Variable Caputo-Fabrizio scheme, considering diverse stochastic scenarios of control constraints. Following this, we craft a parametric model using a Radial basis function neural network under various initial conditions and variable order of the generalized variable order Volta's system. We compute diverse manifestations of chaos within Volta's system using a dynamical neural network structure across different fractional order solutions. The phase portrait of the chaotic attractor demonstrates the chaotic behavior of the generalized variable order fractional Volta system through the Lyapunov exponent. We calculate time delay and embedded dimension using the Average Mutual Information (AMI) method to reconstruct the phase space for generalized variable order Volta's system. The proposed configuration of the Radial basis function neural network has been verified as an exceptionally effective tool for both soft computing and dynamics analysis of chaotic systems within the variable order fractional domain.

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“…Fractional-order models have found applications and extensions in various domains, including circuit systems [24], ecological models [25][26][27], rheology [28], control engineering [29], reflection diffusion [30], and chaos models [31]. Fractional derivatives offer a more realistic depiction as they consider the entire time region of a biological process, whereas integer derivatives only capture changes at specific points in time [26].…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamics Analysis and Chaos Control of a Fractional-Order Three-Population Food Chain Model

Cui

Zhou

2023

Fractal Fract

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The present study investigates the stability analysis and chaos control of a fractional-order three-population food chain model. Previous research has indicated that the predation relationship within a long-established predator–prey system can be influenced by factors such as the prey’s fear of the predator and its carry-over effects. This study examines the state evolution of fractional-order systems and compares their dynamic behavior with integer-order systems. By utilizing the Routh–Hurwitz condition and the stability theory of fractional differential equations, this paper establishes the local stability conditions of the model through the application of the Jacobi matrix and eigenvalue method. Furthermore, the conditions for the Hopf bifurcation generation are determined. Subsequently, chaos control techniques based on the Lyapunov stability theory are employed to stabilize the unstable trajectory at the equilibrium point. The theoretical findings are validated through numerical simulations. These results enhance our understanding of the stability properties and chaos control mechanisms in fractional-order three-population food chain models.

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On Variable-Order Fractional Discrete Neural Networks: Existence, Uniqueness and Stability

Cited by 14 publications

References 31 publications

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

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

Optimizing Nonlinear Variable Fractional Volta’s System Design with RBFNN-Enhanced Intelligence Computing Networks

Complex Dynamics Analysis and Chaos Control of a Fractional-Order Three-Population Food Chain Model

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