Synchronous Stability of Two Photosensitive Neurons Coupled by Nonlinear Synapse

doi:10.19596/j.cnki.1001-246x.8807

Abstract

Abstract:

A phototube is connected to a simple neural circuit for developing a light-sensitive neural circuit, which can be regulated to trigger suitable firing modes by taming the frequency or amplitude of external stimulus. Furthermore, the photoelectric neuron and its Hamilton energy are obtained through scale transformation. It is discerned that the firing modes of neuron is dependent on the energy level of the neuron. Chaotic signals are filtered and encoded to excite the neuron, then chaotic firing modes are obtained and the modes transition and energy value are changed significantly by increasing the intensity of the filtered signals from chaotic system. Considering the complexity and plasticity of the synapse, a nonlinear resistor is used to couple two photosensitive neural circuits. The synchronization stability and energy exchange between two coupled neurons presenting with different initial firing modes are investigated by applying periodic and filtered signals on the neurons. Furthermore, additive noise is applied to investigate the synchronization stability and energy propagation between the two neurons. When photocurrent is selected in periodic type, two coupled neurons are blocked to reach complete synchronization, the coupling intensity is fluctuated with time and energy balance is broken between two neurons. By taming the noise intensity, two bursting neurons can reach complete synchronization while two chaotic neurons seldom reach synchronization when the neurons are driven by peridic currents. When filtered signals are used to excite the two coupled neurons, intermittent phase lock and phase synchronization can be realized between two neurons.

Key words: photosensitive neuron, energy distribution, nonlinear synapse, zynchronization

Yanni LI, Chunni WANG. Synchronous Stability of Two Photosensitive Neurons Coupled by Nonlinear Synapse[J]. Chinese Journal of Computational Physics, 2025, 42(1): 106-117.

Figures/Tables 10

Fig.1 Schematic diagram of photosensitive neural circuit

Fig.2 Photoelectric neural circuits coupled by nonlinear resistor

Fig.3 Bifurcation, Hamilton energy and energy proportion of single neural circuit driven by periodic signals (a) bifurcation diagram of ISI vs. the frequency of the periodic stimulus signal (The small image in the figure is a partial enlargement.); (b) dependence of Hamilton energy on frequency of the Periodic stimulus signal; (c) evolution of the electric energy proportion PC and the magnetic energy proportion PL vs. frequency of the periodic stimulus signal (a=0.7, b=0.8, c=0.1, ζ=0.25, A=0.6, the initial value is [0.2, 0.1].)

Fig.4 Sampled time series of membrane potential, attractor, the Hamilton energy and evolution of the ratio P between electric field energy and magnetic field energy of single neuron circuit stimulated by periodic photocurrents of different frequencies ω (a) ω=0.01; (b) ω=0.1; (c) ω=0.81 (a=0.7, b=0.8, c=0.1, ζ=0.25, A=0.6. The initial value is [0.2, 0.1].)

Fig.5 Mode transition, CV distribution and energy evolution of neuron driven by filtered photocurrent signal (a) bifurcation diagram of ISI vs. E. (b) CV vs. E.(c) H vs. E. (d)~(f) are sampled time series of membrane potential (the small image in the figure is the corresponding phase diagram.), Hamiltonian energy H and ratio P of electric field energy to magnetic field energy of neuronal circuit with different amplitude E of filtered photocurrent signal; (d) E=0.69; (e) E=1.43; (f) E=8.4 (a=0.7, b=0.8, c=0.1, ζ=0.25, α=9.78, β=14.97, γ=0.0, m0=-1.31, m1=-0.75. The initial value is [0.1, 0.1, 1, 0.2, 0.1].)

Fig.6 Evolution of energy difference, synchronization error function, phase error, coupling intensity and coupling channel energy consumption of two coupled neurons with different initial states driven by period photocurrent with different frequency (a) bursting pattern, ω=0.01;(b) spiking pattern, ω=0.1;(c) chaos pattern, ω=0.81 (A=0.6, a=0.7, b=0.8, c=0.1, ζ=0.25. The initial value is [0.2, 0.1, 0.02, 0.01].)

Fig.7 Effect of noise on synchronization state of two coupled bursting neurons (a) D=0.05;(b) D=0.2;(c) D=2.0 (ω=0.01, A=0.6, a=0.7, b=0.8, c=0.1, ζ=0.25.The initial value is [0.2, 0.1, 0.02, 0.01].)

Fig.8 Evolution of energy diversity, error function, phase error, coupling intensity and coupling channel energy consumption in two coupled neuronal circuit with chaotic discharge driven by noise and periodic stimulus (a) D=0.05;(b) D=0.3; (c) D=1.8 (ω=0.81, A=0.6, a=0.7, b=0.8, c=0.1, ζ=0.25. The initial value is [0.2, 0.1, 0.02, 0.01].)

Fig.9 Evolution of energy diversity, error function, phase error, coupling intensity and coupling channel energy consumption in the two coupled neurons by the filtered chaotic photocurrent (a)E=0.69; (b)E=1.43; (c)E=8.4 (a=0.7, b=0.8, c=0.1, ζ=0.25, α=9.78, β=14.97, γ=0.0, m0=-1.31, m1=-0.75. The initial value is[0.1, 0.1, 1, 0.2, 0.1, 0.02, 0.01].)

Fig.10 Evolution of energy diversity, error function, phase error, coupling intensity and energy consumption of two coupled neurons driven by filtered chaotic photocurrent with noise (a)D=0.04; (b)D=1.0; (c)D=4.0 (E=0.69, a=0.7, b=0.8, c=0.1, ζ=0.25, α=9.78, β=14.97, γ=0.0, m0=-1.31, m1=-0.75. The initial value is [0.1, 0.1, 1, 0.2, 0.1, 0.02, 0.01].)

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