Related papers: Folded Bifurcation in Coupled Asymmetric Logistic …
We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also…
In this study, we investigate the occurrence of a three-frequency quasiperiodic torus in a three-dimensional Lotka-Volterra map. Our analysis extends to the observation of a doubling bifurcation of a closed invariant curve, leading to a…
We investigate dynamical systems obtained by coupling two maps, one of which is chaotic and is exemplified by an Anosov diffeomorphism, and the other is of gradient type and is exemplified by a N-pole-to-S-pole map of the circle. Leveraging…
A novel flow state consisting of two oppositely travelling waves (TWs) with oscillating amplitudes has been found in the counterrotating Taylor-Couette system by full numerical simulations. This structure bifurcates out of axially standing…
With the recent development of analytical methods for studying the collective dynamics of coupled oscillator systems, the dynamics of communities of coupled oscillators have received a great deal of attention in the nonlinear dynamics…
We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the…
The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally…
This paper compares three different types of ``onset of chaos'' in the logistic and generalized logistic map: the Feigenbaum attractor at the end of the period doubling bifurcations; the tangent bifurcation at the border of the period three…
A coupled map model for the chaotic phase synchronization and its desynchronization phenomenon is proposed. The model is constructed by integrating the coupled kicked oscillator system, kicking strength depending on the complex state…
We study the synchronization of $N$ nearest neighbors coupled oscillators in a ring. We derive an analytic form for the phase difference among neighboring oscillators which shows the dependency on the periodic boundary conditions. At…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
This paper studies bifurcations in a three node power system when excitation limits are considered. This is done by approximating the limiter by a smooth function to facilitate bifurcation analysis. Spectacular qualitative changes in the…
Highly symmetric networks can exhibit partly symmetry-broken states, including clusters and chimera states, i.e., states of coexisting synchronized and unsynchronized elements. We address the $\mathbb{S}_4$ permutation symmetry of four…
We study the dynamics of billiard models with a modified collision rule: the outgoing angle from a collision is a uniform contraction, by a factor lambda, of the incident angle. These pinball billiards interpolate between a one-dimensional…
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…
We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos' manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets…
Objects driven through periodically modulated potential-energy landscapes in two dimensions can become locked in to symmetry-selected directions that are independent of the driving force's orientation. We investigate this problem in the…
We study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps, interacting with random delay times. Four different types of topologies are investigated: two regular (a ring-type and a…
Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The…
An important challenge in several disciplines is to understand how sudden changes can propagate among coupled systems. Examples include the synchronization of business cycles, population collapse in patchy ecosystems, markets shifting to a…