Brain res bull

The nervous system is composed of a large number of neurons, and the electrical activities of neurons can present multiple modes during the signal transmission between neurons by changing intrinsic bifurcation parameters or under appropriate external forcing. In this review, the dynamics for neuron, neuronal network is introduced, for example, the mode transition in electrical activity, functional role of autapse connection, bifurcation verification in biological experiments, interaction between neuron and astrocyte, noise effect, coherence resonance, pattern formation and selection in network of neurons. Finally, some open problems in this field such as electromagnetic radiation on electrical activities of neuron, energy consumption in neurons are presented.

A review for dynamics of collective behaviors of network of neurons

Applications of stochastic resonance to machinery fault detection: A review and tutorial

Neural networks have been applied in various fields from signal processing, pattern recognition, associative memory to artificial intelligence. Recently, nanoscale memristor has renewed interest in experimental realization of neural network. A neural network with a memristive synaptic weight is studied in this work. Dynamical properties of the proposed neural network are investigated through phase portraits, Poincare map, and Lyapunov exponents. Interestingly, the memristive neural network can generate hyperchaotic attractors without the presence of equilibrium points. Moreover, circuital implementation of such memristive neural network is presented to show its feasibility.

A novel memristive neural network with hidden attractors and its circuitry implementation

Autapse connected to the neuron can change the electric activity of neuron. The effect of autapse on neuronal activity is often described by adding an additive forcing current along a close loop, which is described by a time-delayed feedback on the membrane potential. Neuron often responds to electric autapse forcing sensitively and quickly, while the chemical autapse changes the electric activity of neuron slowly. By applying external forcing, a shift transition of electric activity can be more easily induced by the electric autapse than the chemical autapse. Our results confirm that chemical autapse can enhance and/or suppress the transition of electric activity with excitable or inhibitory type driven by electric autapse, vice versa. It indicates that an appropriate switch-off-on for autapse can make the neuron give different types of response to external forcing. Particularly, cooperation and competition between chemical and electric autapse help neuron response to external forcing in the most reliable way.

Transition of electric activity of neurons induced by chemical and electric autapses

The method of moments is applied to an underdamped bistable oscillator driven by Gaussian white noise and a weak periodic force for the observations of stochastic resonance and the resulting resonant structures are compared with those from Langevin simulation. The physical mechanisms of the stochastic resonance are explained based on the evolution of the intrawell frequency peak and the above-barrier frequency peak via the noise intensity and the fluctuation-dissipation theorem, and the three possible sources of stochastic resonance in the system are confirmed. Additionally, with the noise intensity fixed, the stochastic resonant structures are also observed by adjusting the nonlinear parameter.

Observing stochastic resonance in an underdamped bistable Duffing oscillator by the method of moments.

Using Fourier analysis as tool, we prove that the Caputo fractional-order derivative of the non-constant periodic function cannot be periodic, and thus we confirm the nonexistence of the non-constant exact periodic solutions in a class of the Caputo fractional-order initial-valued dynamical systems (including the autonomous case) from a different viewpoint. We also demonstrate with theoretical discussion and numerical examples that the non-constant long-time periodic solution might exist in the Caputo fractional-order systems. The investigation clarifies the difference and similarity of the periodic solutions between the Caputo fractional-order dynamical systems and the integer-order dynamical systems in a systematic way.

On the nonexistence of non-constant exact periodic solutions in a class of the Caputo fractional-order dynamical systems

We find that the fractional-order Hindmarsh-Rose model neuron demonstrates various types of firing behavior as a function of the fractional order in this study. There exists a clear difference in the bifurcation diagram between the fractional-order Hindmarsh-Rose model and the corresponding integer-order model even though the neuron undergoes a Hopf bifurcation to oscillation and then starts a period-doubling cascade to chaos with the decrease of the externally applied current. Interestingly, the discharge frequency of the fractional-order Hindmarsh-Rose model neuron is greater than that of the integer-order counterpart irrespective of whether the neuron exhibits periodic or chaotic firing. Then we demonstrate that the firing behavior of the fractional-order Hindmarsh-Rose model neuron has a higher complexity than that of the integer-order counterpart. Also, the synchronization phenomenon is investigated in the network of two electrically coupled fractional-order model neurons. We show that the synchronization rate increases as the fractional order decreases.

Firing properties and synchronization rate in fractional-order Hindmarsh-Rose model neurons

Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise

Suprathreshold stochastic resonance (SSR) is examined in the context of integrate-and-fire neurons, with an emphasis on the role of correlation in the neuronal firing. We employed a model based on a network of spiking neurons which received synaptic inputs modeled by Poisson processes stimulated by a stepped input signal. The smoothed ensemble firing rate provided an output signal, and the mutual information between this signal and the input was calculated for networks with different noise levels and different numbers of neurons. It was found that an SSR effect was present in this context. We then examined a more biophysically plausible scenario where the noise was not controlled directly, but instead was tuned by the correlation between the inputs. The SSR effect remained present in this scenario with nonzero noise providing improved information transmission, and it was found that negative correlation between the inputs was optimal. Finally, an examination of SSR in the context of this model revealed its connection with more traditional stochastic resonance and showed a trade-off between supratheshold and subthreshold components. We discuss these results in the context of existing empirical evidence concerning correlations in neuronal firing.

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Yan-Mei Kang

Papers

Observing stochastic resonance in an underdamped bistable Duffing oscillator by the method of moments.

On the nonexistence of non-constant exact periodic solutions in a class of the Caputo fractional-order dynamical systems

Firing properties and synchronization rate in fractional-order Hindmarsh-Rose model neurons

Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise

Suprathreshold stochastic resonance in neural processing tuned by correlation.