Related papers: Isochronous bifurcations in a two-parameter twist …
We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with non-hierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border…
The effect of multiplicative stochastic perturbations on Hamiltonian systems on the plane is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates…
A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the…
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…
Generic Hamiltonian systems have a mixed phase space, where classically disjoint regions of regular and chaotic motion coexist. We present an iterative method to construct an integrable approximation, which resembles the regular dynamics of…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show that two-dimensional continuous piecewise-linear maps near…
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…
We study the effect of changes in the parameters of a two-dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical…
We present a quantitative semiclassical treatment of the effects of bifurcations on the spectral rigidity and the spectral form factor of a Hamiltonian quantum system defined by two coupled quartic oscillators, which on the classical level…
The destruction of regular regions in two-dimensional, area-preserving maps is traditionally described in terms of the breakup of invariant curves and the persistence of transport barriers. Here, we investigate how this scenario changes…
The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium of the…
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…
In nontwist systems, primary shearless curves act as barriers to chaotic transport. Surprisingly, the onset of secondary shearless curves has been reported in a few twist systems. Meanwhile, we found that, in twist systems, the onset of…
We introduce a criterion for the existence of regular states in systems with a mixed phase space. If this condition is not fulfilled chaotic eigenstates substantially extend into a regular island. Wave packets started in the chaotic sea…
In [5] the structure of the bifurcation diagrams of a class of superlinear indefinite problems with a symmetric weight was ascertained, showing that they consist of a primary branch and secondary loops bifurcating from it. In [4] it has…
Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phases wrap around the circle in a linear fashion. Here, we…
Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small…
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest neighbor interactions,…