Reproduce the biophysical function of chemical synapse by using a memristive synapse

Dynamical modeling of nervous systems is of fundamental importance in many scientific fields containing the topics relative to computational neuroscience and biophysics. Many feasible mathematical models have been suggested in the explanation and prediction of some features of neural activities. Considering the special experimental findings and the computational efficiency, it is necessary to find a perfect balance between estimating biophysical functions with complete dynamics and reducing complexity when a tractable model is built. In this paper, a chemical synaptic model is reproduced by using a memristive synapse because it not only remains synaptic characteristic but also exhibits a pinched hysteresis loop and active feature locally. That is, a neuron activated by chemical synapse can produce similar firing modes as the neuron coupled by a memristive synapse, and both the chemical synapse and memristive synapse have similar field effect and biophysical properties. By calculating the one-parameter and two-parameter bifurcation as well as the Lyapunov exponent spectrum, it is confirmed that a neuron can be excited by the chemical synapse or the memristive synapse for generating chaotic firing patterns. Oscillation of the circuit composed of neuron and functional synapse is analyzed, suggesting that there exists a relation between the local activity and the edge of chaos via Hopf bifurcation. A modular circuit is designed to construct large-scale neural network. These results in this paper provide new evidences for application of memristive components and guide us to know the biophysical function of chemical synapse from physical viewpoint, in which the chemical synapse could be a kind of memristive synapse because of the same biophysical function.