RESUMEN
Chimera states refer to the dynamical states in which the inherent symmetry of the system is broken. The system composed of two interacting identical subpopulations of phase oscillators provides a platform to study chimera states. In this system, different types of chimera states have been identified and the transitions between them have been investigated. However, the parameter space is not fully explored in this system. In this work, we study a system comprised of two interacting subpopulations of nonidentical phase oscillators. Through numerical simulations and theoretical analyses, we find three symmetry-reserving states, including incoherent state, in-phase synchronous state, and antiphase synchronous state, and three types of symmetry-breaking states, including in-phase chimera states, antiphase chimera states, and weak chimera states. The stability diagrams of these dynamical states are explored on different parameter planes and transition scenarios amongst these states are investigated. We find that the weak chimera states act as the bridge between in-phase and antiphase chimera states. We also observe the existence of a period-two chimera state, chaotic chimera state, and drifting chimera states.
RESUMEN
In this work, we study the Kuramoto model with biharmonic interaction and bimodal frequency distribution. Rich synchronous dynamics, such as standing wave states, stationary partial synchronous dynamics, and multiplicity of singular synchronous dynamics, are found. Notably, we find a symmetry-breaking synchronous dynamics when the peaks in frequency distribution are not well separated. We present the phase diagrams for two cases: the peaks in the frequency distribution are well separated and the peaks are not well separated. We find that reducing peak distance tends to make the transition between standing wave states and stationary partial synchronous states to be continuous when the multiplicity of singular synchronous state is present or to be discontinuous when the multiplicity is absent.
RESUMEN
We investigate a Deffuant model on a ring by introducing two modifications: the repelling mechanism and the circular opinions. The repelling mechanism drives the opinions of two individuals away from each other and the circular opinions are defined on a circle. We find that the repelling mechanism tends to polarize the opinions of adjacent individuals and the circular opinions bring up a spatiotemporal pattern in which all individuals take different opinions but the opinion difference between two neighboring individuals tends to zero in the limit of the population size. In the Deffuant model with both repelling mechanism and the circular opinions, opinion dynamics depends on both the bounded confidence and the convergence rate. The interplay between the repelling mechanism and the circular opinion may give rise to time-dependent opinion dynamics.
