相关论文: Emergence and evolution of unusual inhomogeneous l…

Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…

We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…

In this paper, we explore the three-dimensional chaotic set near a homoclinic cycle to a hyperbolic bifocus at which the vector field has negative divergence. If the invariant manifolds of the bifocus satisfy a non-degeneracy condition, a…

This report unravels frustration as a source of transient chaotic dynamics even in a simple array of coupled limit cycle oscillators. The transient chaotic dynamics along with the multistable nature of frustrated systems facilitates the…

Numerous biological systems exhibit transitions to synchronised oscillations via a population-density-dependant mechanism known as quorum sensing. Here we propose a model system, based on spatially distributed limit-cycle oscillators, that…

We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic…

We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…

We investigate the maximum number of limit cycles bifurcating from the period annulus of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic piecewise smooth polynomials. The family…

We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-…

A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz.…

We study the spatio-temporal dynamics of the generalized repressilator, a system of coupled repressing genes arranged in a directed ring topology, and give analytical conditions for the emergence of a cascade of unstable periodic orbits…

We develop a framework for the general interpretation of the stochastic dynamical system near a limit cycle. Such quasi-periodic dynamics are commonly found in a variety of nonequilibrium systems, including the spontaneous oscillations of…

Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…

This paper investigates the exact number of limit cycles given by the averaging theory of first order for the piecewise smooth integrable non-Hamiltonian system \begin{eqnarray*} (\dot{x},\ \dot{y})=\begin{cases} (-y(x+a)^2+\varepsilon…

Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…

Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…

We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order…

We predict the limit cycle solution for a ring-shape bosonic condensate of exciton-polaritons confined in an optically induced rotating trap. The limit cycle manifests itself with polarization oscillations on a characteristic timescale of…

We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…

A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a…