Complex Motion Behavior and Synchronization Analysis of Heterogeneous Neural Network

The study on the dynamical behaviors of the coupled heterogeneous neural network, including bifurcation orbits, synchronization, especially unstable firing behaviors, may have great significance for diagnosis and guarding against brain diseases. To investigate this matter in depth, the discrete implicit mapping method can be employed for assessing the neural network, which is coupled with the Hindmarsh-Rose and FitzHugh-Nagumo neuron models in this paper. The bifurcation trees of periodic motions, exhibiting intricate dynamic behaviors, are precisely demonstrated by maniputing the coupling strength. The transitions from period-1 to period-8, period-3 to period-12, period-4 to period-16 and period-5 to period-10 will be achieved through saddle bifurcations and period doubling bifurcations. The corresponding stable firing patterns are observed through discrete nodes in phase diagrams, time-histories and deviations of the membrane potential diagrams. Meanwhile, the unstable firing patterns, using the particular method, are also obtained, which cannot be calculated through the numerical method due to its accumulative errors. Moreover, the synchronous and asynchronous behaviors depending on the coupling strength are successively revealed and described. Lastly, the experiment of the heterogeneous neural network is validated by the field-programmable gate array (FPGA) circuit. Such an investigation will also positively contribute to the development of the progress of brain medicine and life science and engineering.