Generalized synchronization of the extended Hindmarsh–Rose neuronal model with fractional order derivative

Giresse, Tene Alain; Crépin, Kofané Timoléon; Tchoffo, Martin

doi:10.1016/j.chaos.2018.11.028

Cited by 26 publications

(19 citation statements)

References 37 publications

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“…The dynamic characteristics of this extended HR neuronal model have been verified to be consistent with the biological characteristics of neurons [11], [12]. Therefore, this improved HR neuronal model is appropriate for the theoretical and computational study of the firing properties and synchronization behaviors of neurons [13], [14].…”

Section: Introductionmentioning

confidence: 54%

“…For the external input I ext , a direct current has been widely considered in the literature [13], [14], [17], [21]. However, in neuroscience, many noninvasive transcranial stimulation methods, such as TMS, TFUS, and TMAS, generate alternating currents to stimulate neurons.…”

Section: The Extended Hindmarsh-rose Neuronal Model With the Modelmentioning

confidence: 99%

“…For example, Yong et al investigated the effect of the fractional order on the firing modes by numerical and simulation analyses and generalized the chaotic characteristics of the fractionalorder HR neuronal model [17]. Giresse et al designed a control scheme for the synchronization of FOEHR neuronal models [14]. It is worth noting that these studies consider only direct currents as the external inputs.…”

Section: Introductionmentioning

confidence: 99%

“…In [13], a feedback synchronization controller was designed for the fractional-order HR neuronal model, whose gain is limited by certain parameter conditions. Later, the authors of [14] designed controllers for the synchronized behavior of coupled fractional-order extended HR neurons. However, these controllers rely on all of the model parameters, this is too strict a requirement for the HR neuronal model, which has uncertain parameters.…”

Section: Introductionmentioning

confidence: 99%

“…3) The neuron system is assumed to be subject to uncertain model parameters and unknown external disturbances. With the proposed method, the neuronal models can achieve GPS in a finite amount of time and are resilient to uncertain parameters and external disturbances, which are not considered in [14], [32].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Adaptive Fuzzy Control for the Generalized Projective Synchronization of Fractional-Order Extended Hindmarsh-Rose Neurons

2020

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We investigate the generalized projective synchronization (GPS) control of fractional-order extended Hindmarsh-Rose (FOEHR) neuronal models with transcranial magneto-acoustical stimulation (T-MAS) input. This improved neuronal model has advantages in describing the complex firing characteristics of neurons stimulated by alternating current. In this study, a master-slave neuron system consisting of two FOEHR neuronal models is assumed to be subject to uncertain model parameters and unknown external disturbances. To quantify the GPS error, we design a new error variable based on the properties of the fractional-order derivative and construct a related GPS error system. Fuzzy logic systems are introduced to approximate the unknown nonlinear dynamics of the error system. To ensure the synchronous firing rhythms of the master-slave neuron system, an adaptive fuzzy control algorithm is proposed under the Lyapunov approach, in which the adaptive parameters are robust to the estimation errors. By choosing the appropriate design parameters, the proposed control scheme enables the master-slave neuron system to achieve GPS in a finite amount of time and to be resilient to uncertain parameters and unknown disturbances. The simulation results demonstrate that after the designed control inputs are implemented, the states of the slave neuron synchronize with those of the master neuron in specified proportions, and the corresponding synchronization error converges towards an arbitrarily small neighborhood of zero. INDEX TERMS Generalized projective synchronization, fractional-order, extended Hindmarsh-Rose neuronal model, fuzzy logic system.

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Section: Introductionmentioning

confidence: 54%

Section: The Extended Hindmarsh-rose Neuronal Model With the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive Fuzzy Control for the Generalized Projective Synchronization of Fractional-Order Extended Hindmarsh-Rose Neurons

2020

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Wavelet Analysis of the Non-stationary Rose-Hindmarsh Model Describing Neural Activity

Bozhokin

2021

Advances in Neural Computation, Machine Learning, and Cognitive Research V

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Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model

et al. 2019

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In this paper, the extended Hindmarsh-Rose neuron model, which considers the slow intracellular exchange of calcium ions between its store and the cytoplasm, is studied. The dynamical behavior of this neuron model is analyzed by deriving the equilibrium points, the bifurcation diagrams, and the Lyapunov exponents, in the presence of an external forcing current. Furthermore, the dynamics of the network of the extended model is investigated. Firstly, a one-dimensional ring network is constructed, and the effects of the coupling strength and the forcing current are considered on the network behavior. The results confirm the existence of chimera state in small coupling strength values. Then a square network of the proposed model is created by adding an external excitation to the neurons

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Generalized synchronization of the extended Hindmarsh–Rose neuronal model with fractional order derivative

Cited by 26 publications

References 37 publications

Adaptive Fuzzy Control for the Generalized Projective Synchronization of Fractional-Order Extended Hindmarsh-Rose Neurons

Adaptive Fuzzy Control for the Generalized Projective Synchronization of Fractional-Order Extended Hindmarsh-Rose Neurons

Wavelet Analysis of the Non-stationary Rose-Hindmarsh Model Describing Neural Activity

Dynamical behavior and network analysis of an extended Hindmarsh–Rose neuron model

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