Research On Some Problems In Spiking Neuron Circuits Networks

As the third artificial neural networks, spiking neural networks are closer to biological model and are paid more attention to. Spiking neuron circuit (SNC) and pulse-coupled spiking neuron circuits networks (PCSNC) consisting of SNCs have rich nonlinear characteristics. Therefore, it is meaningful to investigate the dynamics of them. In this paper, firstly, the effect of pulse width on the dynamics of SNC and PCSNC is analyzed. Then a new kind of SNC model called spiking neuron circuit with double two signals (SNCD) is put forward. The dynamics of SNCD and pulse-coupled SNCDs (PCSNCD) consisting of SNCDs are investigated. Lastly, the effect of pulse width on the dynamics of SNCD and PCSNCD is researched. The detailed content in this paper is as follows:Firstly, the influences of pulse width on the dynamics of SNC and PCSNC are analyzed in-depth because the pulse width can't be neglected in SNC and PCSNC. By calculating the bifurcation diagram,the distribution diagram of periodic orbits and Lyapunov exponent, it is discovered that pulse width can make single SNC output rich bifurcation phenomena such as period-doubling bifurcation, inverse period-doubling bifurcation, tangent bifurcation and intermittent chaos. Meanwhile, pulse width can change the characteristics of pulse output and alter the parametric regions, where periodic and chaotic pulse trains are generated, respectively.Secondly, a new kind of SNC we call SNCD with two periodic base signals is presented. The formula of inter-spike interval (ISI) about this new model is achieved. Based on ISI, it turns out that the deviation of any parameter in the model may cause rich nonlinearity such as pitchfork bifurcation, saddle-node bifurcation and intermittent chaos for single SNCD. For PCSNCD, it is discovered that small change of any parameter can alter the area, form and position of parametric zone where chaotic and periodic pulse trains are achieved, which demonstrates richer dynamics about the new model.Thirdly, the effects of pulse width on the dynamics of SNCD and PCSNCD are researched in light of the existence for pulse width in SNCD and PCSNCD. Simulation results show that pulse width may cause single SNCD to output periodic and chaotic pulse trains alternatively, which generates rich bifurcation phenomena. Meanwhile, pulse width can alter the area and form of parametric regions, where periodic and chaotic pulse trains are generated and self-similarity structures are produced.