Coupling-induced tunable oscillations in loops of even-numbered bistable systems.

Abstract

Negative couplings and suitable initial conditions can induce asymmetric repulsions in feedback loops of odd-numbered overdamped bistable oscillators, allowing them to switch between stable fixed points and produce sustained oscillations that resemble traveling waves [Phys. Rev. E 68, 045102(R) (2003)1063-651X10.1103/PhysRevE.68.045102]. This study shows that changing negative couplings to positive ones can create symmetric attractions among even-numbered overdamped bistable oscillators, leading to similar travelinglike oscillations. We employ a simple two-state model to elucidate the symmetric initial conditions required for these oscillations and estimate the necessary ranges of coupling strength to maintain them. Additionally, we analyze the relationships between oscillation amplitude and frequency regarding the coupling strength and the model parameter, which are consistent with our numerical results. Our findings enhance the understanding of coupling-induced oscillations.