Related papers: Basin Riddling in Coupled Phase Oscillators
The behaviors of coupled chaotic oscillators before complete synchronization were investigated. We report three phenomena: (1) The emergence of long-time residence of trajectories besides one of the saddle foci; (2) The tendency that orbits…
We consider a population of globally coupled oscillators in which phase shifts in the coupling are random. We show that in the maximally disordered case, where the pairwise shifts are i.i.d. random variables, the dynamics of a large…
We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to…
It is common that the average length of chaotic transients appearing as a consequence of crises in dynamical systems obeys a power low of scaling with the distance from the crisis point. It is, however, only a rough trend; in some cases…
The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at…
We investigate the basin of attraction properties and its boundaries for chimera states in a circulant network of H\'enon maps. Chimera states, for which coherent and incoherent domains coexist, emerge as a consequence of the coexistence of…
Coupled non-linear oscillators are ubiquitous in dynamical studies. A wealth of behaviors have been found mostly for globally coupled systems. From a complexity perspective, less studied have been systems with local coupling, which is the…
The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling…
Traveling waves triggered by a phase slip in coupled map lattices are studied. A local phase slip affects globally the system, which is in strong contrast with kink propagation. Attractors with different velocities coexist, and form…
Fractal basin structure in the two-dimensional dissipative circle map is examined in detail. Numerically obtained basin appears to be riddling in the parameter region where two periodic orbits co-exist near a boundary crisis, but it is…
In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…
Twisted bilayers of two-dimensional materials have emerged as a highly tunable platform for studying broken symmetry phases. While most interest has been focused on emergent states in systems whose constituent monolayers do not feature…
Many oscillator networks are multistable, meaning that different synchronization states are realized depending on the initial conditions. In this paper, we numerically analyze a ring network of phase oscillators, in which synchronous states…
We explore the nonlinear dynamics of a driven power law oscillator whose shape varies periodically in time covering a broad spectrum of anharmonicities. Combining weak and strong confinement of different geometry within a single driving…
We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We…
The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…
A pure quantum state of large number N of oscillators, interacting via harmonic coupling, evolves such that any small subsystem n<<N of the global state approaches equilibrium. This provides a novel example where equilibration emerges as a…
A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle…
We study the dynamics of a swarmalator model with higher harmonic phase coupling. We analyze stability, bifurcation and structural properties of several novel attracting states, including the formation of spatial clusters with distinct…