Synchronization of starlike neural network with electromagnetic autapse under electrical and fast chemical synapses

Multiple interactions with systems are present in the brain and in many other complex systems. However, how to explore their dynamics is still an open problem. Here, we propose a starlike Hopfield neural network (HNN) with multiple interactions involving neurons, electromagnetic autapse, and synapse. There are two classes of the starlike HNNs activated by introducing memristive electromagnetic autaptic (MEA) current at the central and peripheral nodes, respectively. The starlike MEA-HNN models can exhibit the rapid and slack chaotic bursting, dependent upon the modulation of MEA current at different nodes. The initial values in the improved HNN model can control the alternant occurrence of firing patterns between chaotic bursting and resting. It is found that both electrical synapses and chemical synapses can make homogeneous and heterogeneous coupled networks to achieve synchronization. Under the electrical synapse, the bursting-type synchronization is transitioned as periodic synchronization, suggesting that the original firing pattern has been disrupted. While the coupled model is still the bursting synchronization under the chemical synapse. The obtained results can help understand the complexity of neural networks with different structures and the dynamic mechanism of interaction underlying coupled chaotic bursting oscillators.