Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system

Al-Qurashi, Maysaa; Asif, Qurat ul Ain; Chu, Yu‐Ming; Rashid, Saima; Elagan, S. K.

doi:10.1016/j.rinp.2023.106627

Cited by 11 publications

(4 citation statements)

References 44 publications

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“…Fractional chaotic behaviors are extensively seen in both social and natural sciences, attracting considerable interest from various domains. In recent years, discrete-time fractional calculus has attracted much interest due to its significance in real-world challenges [19][20][21][22][23][24][25][26]. These studies have reflected that the system's behavior is highly dependent on the chosen fractional order, showcasing its non-linear and complex nature, which makes it a fascinating subject of study in the field of fractional dynamics.…”

Section: Introductionmentioning

confidence: 99%

On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders

Hamadneh,

Abbes,

Al-Tarawneh

et al. 2023

Mathematics

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In this study, we expand a 2D sine map via adding the discrete memristor to introduce a new 3D fractional-order sine-based memristor map. Under commensurate and incommensurate orders, we conduct an extensive exploration and analysis of its nonlinear dynamic behaviors, employing diverse numerical techniques, such as analyzing Lyapunov exponents, visualizing phase portraits, and plotting bifurcation diagrams. The results emphasize the sine-based memristor map’s sensitivity to fractional-order parameters, resulting in the emergence of distinct and diverse dynamic patterns. In addition, we employ the sample entropy (SampEn) method and C0 complexity to quantitatively measure complexity, and we also utilize the 0–1 test to validate the presence of chaos in the proposed fractional-order sine-based memristor map. Finally, MATLAB simulations are be executed to confirm the results provided.

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Section: Introductionmentioning

confidence: 99%

On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders

Hamadneh,

Abbes,

Al-Tarawneh

et al. 2023

Mathematics

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“…The relevant articles mentioned above indicate the substantial popularity of using a Caputo-type fractional difference operator 19 in the modeling of complex systems via time discreteness. Because DFC has numerous benefits over classical calculus, we need to employ it for investigating NN architectures 20 , 21 . For a pair of explanations, the modeling of NNs with fractional exponents can be utilized for studying neurons in biology.…”

Section: Introductionmentioning

confidence: 99%

“…For a pair of explanations, the modeling of NNs with fractional exponents can be utilized for studying neurons in biology. Initially, by boosting a level of liberation, the FO improves mechanism efficiency 20 , 21 . The memory and heridatory characteristics of several scientific models can be described using the variable-order (VO) fractional operators and their non-stationary power-law kernel.…”

Section: Introductionmentioning

confidence: 99%

Complex adaptive learning cortical neural network systems for solving time-fractional difference equations with bursting and mixed-mode oscillation behaviours

Chu,

Rashid,

Alzahrani

et al. 2023

Sci Rep

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Complex networks have been programmed to mimic the input and output functions in multiple biophysical algorithms of cortical neurons at spiking resolution. Prior research has demonstrated that the ineffectual features of membranes can be taken into account by discrete fractional commensurate, non-commensurate and variable-order patterns, which may generate multiple kinds of memory-dependent behaviour. Firing structures involving regular resonator chattering, fast, chaotic spiking and chaotic bursts play important roles in cortical nerve cell insights and execution. Yet, it is unclear how extensively the behaviour of discrete fractional-order excited mechanisms can modify firing cell attributes. It is illustrated that the discrete fractional behaviour of the Izhikevich neuron framework can generate an assortment of resonances for cortical activity via the aforesaid scheme. We analyze the bifurcation using fragmenting periodic solutions to demonstrate the evolution of periods in the framework’s behaviour. We investigate various bursting trends both conceptually and computationally with the fractional difference equation. Additionally, the consequences of an excitable and inhibited Izhikevich neuron network (INN) utilizing a regulated factor set exhibit distinctive dynamic actions depending on fractional exponents regulating over extended exchanges. Ultimately, dynamic controllers for stabilizing and synchronizing the suggested framework are shown. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.

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“…Alsharidi et al 13 investigated a short-memory discrete fractional difference equation wind turbine model using a Caputo-type fractional difference operator. Al-Qurashi et al 14 expounded the complexity analysis and discrete fractional difference implementation of the Hindmarsh-Rose neuron system. Chu et al 15 derived the new configurations of the fuzzy fractional differential Boussinesq model with application in ocean engineering.…”

Section: Introductionmentioning

confidence: 99%

An advanced approach for the electrical responses of discrete fractional-order biophysical neural network models and their dynamical responses

Chu,

Alzahrani,

Rashid

et al. 2023

Sci Rep

Self Cite

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The multiple activities of neurons frequently generate several spiking-bursting variations observed within the neurological mechanism. We show that a discrete fractional-order activated nerve cell framework incorporating a Caputo-type fractional difference operator can be used to investigate the impacts of complex interactions on the surge-empowering capabilities noticed within our findings. The relevance of this expansion is based on the model’s structure as well as the commensurate and incommensurate fractional-orders, which take kernel and inherited characteristics into account. We begin by providing data regarding the fluctuations in electronic operations using the fractional exponent. We investigate two-dimensional Morris–Lecar neuronal cell frameworks via spiked and saturated attributes, as well as mixed-mode oscillations and mixed-mode bursting oscillations of a decoupled fractional-order neuronal cell. The investigation proceeds by using a three-dimensional slow-fast Morris–Lecar simulation within the fractional context. The proposed method determines a method for describing multiple parallels within fractional and integer-order behaviour. We examine distinctive attribute environments where inactive status develops in detached neural networks using stability and bifurcation assessment. We demonstrate features that are in accordance with the analysis’s findings. The Erdös–Rényi connection of asynchronization transformed neural networks (periodic and actionable) is subsequently assembled and paired via membranes that are under pressure. It is capable of generating multifaceted launching processes in which dormant neural networks begin to come under scrutiny. Additionally, we demonstrated that boosting connections can cause classification synchronization, allowing network devices to activate in conjunction in the future. We construct a reduced-order simulation constructed around clustering synchronisation that may represent the operations that comprise the whole system. Our findings indicate the influence of fractional-order is dependent on connections between neurons and the system’s stored evidence. Moreover, the processes capture the consequences of fractional derivatives on surge regularity modification and enhance delays that happen across numerous time frames in neural processing.

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Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system

Cited by 11 publications

References 44 publications

On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders

On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders

Complex adaptive learning cortical neural network systems for solving time-fractional difference equations with bursting and mixed-mode oscillation behaviours

An advanced approach for the electrical responses of discrete fractional-order biophysical neural network models and their dynamical responses

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