Locally repulsive coupling-induced tunable oscillations.

The precise amplitude and period of neuronal oscillations are crucial for the functioning of neuronal networks. We propose a chain model featuring a repulsive coupling at the first node, followed by attractive couplings at subsequent nodes. This model allows for the simultaneous regulation of both quantities. The repulsive coupling at the first neuron enables it to act as a pacemaker, generating oscillations whose amplitude and period are correlated with the coupling strength. At the same time, attractive couplings help transmit these oscillations along the chain, leading to collective oscillations of varying scales. Our study demonstrates that a three-node chain with locally repulsive coupling forms the fundamental structure for generating tunable oscillations. By using a simplified neuron model, we investigate how locally repulsive coupling affects the amplitude and period of oscillations and find results that align with numerical observations. These findings indicate that repulsive couplings play a crucial role in regulating oscillatory patterns within neuronal networks.