Topology identification and dynamical pattern recognition for Hindmarsh–Rose neuron model via deterministic learning

Chen, Danfeng; Li, Junsheng; Zeng, Wei; He, Jun

doi:10.1007/s11571-022-09812-3

Cited by 4 publications

(1 citation statement)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Te other system parameters take the following values: a � 1, b � 3, c � 1, d � 5, s � 4, r � 0.006, and I � 3.3. Studies on various aspects of the Hindmarsh-Rose model in the continuous case are discussed in [28,[47][48][49]. Synchronization stability of the continuous-time Hindmarsh-Rose has been reported for various choices of coupling schemes [32].…”

Section: Case A: Discrete Hindmarsh-rose Model (Hr)mentioning

confidence: 99%

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Ramasamy,

Kumarasamy,

Sampathkumar

et al. 2023

Complexity

View full text Add to dashboard Cite

In recent times, studies on discrete nonlinear systems received much attention among researchers because of their potential applications in real-world problems. In this study, we conducted an in-depth exploration into the stability of synchronization within discrete nonlinear systems, specifically focusing on the Hindmarsh–Rose map, the Chialvo neuron model, and the Lorenz map. Our methodology revolved around the utilization of the master stability function approach. We systematically examined all conceivable coupling configurations for each model to ascertain the stability of synchronization manifolds. The outcomes underscored that only distinct coupling schemes manifest stable synchronization manifolds, while others do not exhibit this trait. Furthermore, a comprehensive analysis of the master stability function’s behavior was performed across a diverse range of coupling strengths σ and system parameters. These findings greatly enhance our understanding of network dynamics, as discrete-time dynamical systems adeptly replicate the dynamics of continuous-time models, offering significant reductions in computational complexity.

show abstract

Section: Case A: Discrete Hindmarsh-rose Model (Hr)mentioning

confidence: 99%

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Ramasamy,

Kumarasamy,

Sampathkumar

et al. 2023

Complexity

View full text Add to dashboard Cite

show abstract

Efficient digital design of the nonlinear behavior of Hindmarsh–Rose neuron model in large-scale neural population

Nazari,

Jamshidi

2024

Sci Rep

View full text Add to dashboard Cite

Spiking networks, as the third generation of neural networks, are of great interest today due to their low power consumption in cognitive processes. This important characteristic has caused the hardware implementation techniques of spiking networks in the form of neuromorphic systems attract a lot of attention. For the first time, the focus is on the digital implementation based on CORDIC approximation of the Hindmarsh–Rose (HR) neuron so that the hardware implementation cost is lower than previous studies. If the digital design of a neuron is done efficient, the possibility of implementing a population of neurons is provided for the feasibility of low-consumption implementation of high-level cognitive processes in hardware, which is considered in this paper through edge detector, noise removal and image magnification spiking networks based on the proposed CORDIC_HR model. While using less hardware resources, the proposed HR neuron model follows the behavior of the original neuron model in the time domain with much less error than previous study. Also, the complex nonlinear behavior of the original and the proposed model of HR neuron through the bifurcation diagram, phase space and nullcline space analysis under different system parameters was investigated and the good follow-up of the proposed model was confirmed from the original model. In addition to the fact that the individual behavior of the original and the proposed neurons is the same, the functional and behavioral performance of the randomly connected neuronal population of original and proposed neuron model is equal. In general, the main contribution of the paper is in presenting an efficient hardware model, which consumes less hardware resources, follows the behavior of the original model with high accuracy, and has an acceptable performance in image processing applications such as noise removal and edge detection.

show abstract

Physical approach of a neuron model with memristive membranes

Guo,

Wu,

Yang

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

The membrane potential of a neuron is mainly controlled by the gradient distribution of electromagnetic field and concentration diversity between intracellular and extracellular ions. Without considering the thickness and material property, the electric characteristic of cell membrane is described by a capacitive variable and output voltage in an equivalent neural circuit. The flexible property of cell membrane enables controllability of endomembrane and outer membrane, and the capacitive properties and gradient field can be approached by double membranes connected by a memristor in an equivalent neural circuit. In this work, two capacitors connected by a memristor are used to mimic the physical property of two-layer membranes, and an inductive channel is added to the neural circuit. A biophysical neuron is obtained and the energy characteristic, dynamics, self-adaption is discussed, respectively. Coherence resonance and mode selection in adaptive way are detected under noisy excitation. The distribution of average energy function is effective to predict the appearance of coherence resonance. An adaptive law is proposed to control the capacitive parameters, and the controllability of cell membrane under external stimulus can be explained in theoretical way. The neuron with memristive membranes explains the self-adaptive mechanism of parameter changes and mode transition from energy viewpoint.

show abstract

Topology identification and dynamical pattern recognition for Hindmarsh–Rose neuron model via deterministic learning

Cited by 4 publications

References 37 publications

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Efficient digital design of the nonlinear behavior of Hindmarsh–Rose neuron model in large-scale neural population

Physical approach of a neuron model with memristive membranes

Contact Info

Product

Resources

About