Population Dynamics of Randomly Interacting Self-Oscillators. I: Tractable Models without Frustration

Abstract

A class of tractable models for population dynamics with random interactions is proposed which is of the form: for j=1,2, …,N(≫1), where the are independent random parameters and I_j is an interacting neighbor of the site j. Theories of phase transitions to mutual synchronization are developed and verified numerically with particular emphasis on a new type of ordered phase characterized by a vanishing order parameter. The frustration effect is also discussed in the context of population dynamics.