Hindmarsh-Rose neuron model with memristors

Usha, K.; Subha, P. A.

doi:10.1016/j.biosystems.2019.01.005

Cited by 55 publications

(7 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When neuron membrane potential is affected by the external magnetic field, induced current will react on the neuron membrane potential. This kind of influence can be described by a flux-controlled memristor [34].…”

Section: Model Descriptionmentioning

confidence: 99%

Coexisting Firing Patterns in an Improved Memristive Hindmarsh–Rose Neuron Model with Multi-Frequency Alternating Current Injection

Wang,

Ding,

Deng

et al. 2023

Micromachines

View full text Add to dashboard Cite

With the development of memristor theory, the application of memristor in the field of the nervous system has achieved remarkable results and has bright development prospects. Flux-controlled memristor can be used to describe the magnetic induction effect of the neuron. Based on the Hindmarsh–Rose (HR) neuron model, a new HR neuron model is proposed by introducing a flux-controlled memristor and a multi-frequency excitation with high–low frequency current superimposed. Various firing patterns under single and multiple stimuli are investigated. The model can exhibit different coexisting firing patterns. In addition, when the memristor coupling strength changes, the multiple stability of the model is eliminated, which is a rare phenomenon. Moreover, an analog circuit is built to verify the numerical simulation results.

show abstract

Section: Model Descriptionmentioning

confidence: 99%

Coexisting Firing Patterns in an Improved Memristive Hindmarsh–Rose Neuron Model with Multi-Frequency Alternating Current Injection

Wang,

Ding,

Deng

et al. 2023

Micromachines

View full text Add to dashboard Cite

show abstract

“…The phase synchronization of neurons coupled through memristor synapses was also discussed [18]. Compared with the previously proposed memristive neuron systems [19][20][21], the memristive HR system designed in this paper can realize the control of the amount of spiking by altering the synaptic strength of the memristor. This system can achieve single-spike, twospike, three-spike, four-spike, and chaotic firing, respectively.…”

Section: Introductionmentioning

confidence: 99%

Neural Chaotic Oscillation: Memristive Feedback, Symmetrization, and Its Application in Image Encryption

Huang,

Li,

et al. 2024

Electronics

View full text Add to dashboard Cite

The symmetry of neuron discharging has some relationship with the electrophysiological characteristics and dynamic behavior of a neuron, and has a close relation with the symmetry of ion channels, current balance, neuron type, synaptic transmission, and network effects. Among them, the feedback and interactions in the network have a particularly direct impact on the symmetrical discharge of a neuron element. This work introduces a memristor as a synapse into a neuron cell, taking the membrane potential back to ion channels, and therefore various symmetric firing behaviors of Hindmarsh–Rose (HR) neurons are observed, including chaos and various periodic firings. By further adjusting the feedback, coexisting symmetrical discharge of the neuron is achieved. Furthermore, the impact of frequency variations on the memristor synapse is analyzed, and thus the operating regimes of memristor and resistor are classified and discussed. Circuit simulations prove the neural chaotic firings along with their symmetrized discharging processes, demonstrating the effectiveness of symmetrical control of chaotic discharge. Finally, applying the symmetrical system to DNA image encryption can effectively protect the security of images.

show abstract

“…Taking into account the electric field effects aroused by variations in charge distribution and polarization, reference [34] found a neuron model on the basis of HR neuron, and confirmed that the electrical activity of neurons will go through unalike modal transitions. Usha and Subha [35] analyzed the bifurcation pattern of HR neuron model with magnetic flux variable, and studied the coexisting behavior of spiking firing and resting state. Wang et al [36] presented a HR neuron with one time delay and analyzed spiking and bursting behaviors and Hopf bifurcation.…”

Section: Introductionmentioning

confidence: 99%

“…Reference [37] found an extended HindMarsh-Rose neuron with diversity of bifurcations. In these HR neuron models, various biological neuroelectric phenomena have been reported, such as firing activity [32][33][34], spiking states [35], bursting behaviors [36], and multistability [37], which greatly facilitate the development of neurodynamics.…”

Section: Introductionmentioning

confidence: 99%

Four-dimensional Hindmarsh–Rose neuron model with hidden firing multistability based on two memristors

Yan¹,

Zhang²,

Yu³

et al. 2022

Phys. Scr.

View full text Add to dashboard Cite

Since memristors can be used to describe electromagnetic induction effects, this paper proposes a novel 4-D Hindmarsh-Rose (HR) neuron model based on two flux-controlled memristors to show complex dynamics of neuronal electrical activity. It has no equilibrium point, revealing hidden dynamical behaviors. The complex dynamics of the system are illustrated by phase portraits, the time sequences, bifurcation diagrams, and Lyapunov exponents spectra. The presented 4-D HR neuron model can produce coexisting multiple hidden firing patterns, for instance, periodic spiking, chaotic spiking, transient chaotic spiking, periodic bursting, chaotic bursting, transient chaotic bursting, stochastic bursting, and transient stochastic bursting. Besides, rich nonlinear dynamics, such as anti-monotonicity and initial offset boosting, are also found. Finally, Multisim circuit simulation is performed and the results are in accordance with numerical simulation.

show abstract

Hindmarsh-Rose neuron model with memristors

Cited by 55 publications

References 42 publications

Coexisting Firing Patterns in an Improved Memristive Hindmarsh–Rose Neuron Model with Multi-Frequency Alternating Current Injection

Coexisting Firing Patterns in an Improved Memristive Hindmarsh–Rose Neuron Model with Multi-Frequency Alternating Current Injection

Neural Chaotic Oscillation: Memristive Feedback, Symmetrization, and Its Application in Image Encryption

Four-dimensional Hindmarsh–Rose neuron model with hidden firing multistability based on two memristors

Contact Info

Product

Resources

About