Related papers: Non-smooth saddle-node bifurcations III: strange a…
We study a discrete non-autonomous system whose autonomous counterpart (with the frozen bifurcation parameter) admits a saddle-node bifurcation, and in which the bifurcation parameter slowly changes in time and is characterized by a sweep…
It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked…
Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a…
We study the effect of external forcing on the saddle-node bifurcation pattern of interval maps. By replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both for random forcing…
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…
In this work, we consider a class of $n$-dimensional, $n\geq2$, piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may…
We show that it is possible to devise a large class of skew--product dynamical systems which have strange nonchaotic attractors (SNAs): the dynamics is asymptotically on fractal attractors and the largest Lyapunov exponent is nonpositive.…
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation.…
We investigate a typical aerofoil section under dynamic stall conditions, the structural model is linear and the aerodynamic loading is represented by the Leishman-Beddoes semi-empirical dynamic stall model. The loads given by this model…
The existence of non-continuous invariant graphs (or strange non-chaotic attractors) in quasiperiodically forced systems has generated great interest, but there are still very few rigorous results about the properties of these objects. In…
Aperiodic dynamics which is nonchaotic is realized on Strange Nonchaotic attractors (SNAs). Such attractors are generic in quasiperiodically driven nonlinear systems, and like strange attractors, are geometrically fractal. The largest…
Strange nonchaotic attractors (SNAs) in noise driven systems are investigated. Before the transition to chaos, due to the effect of noise, a typical trajectory will wander between the periodic attractor and its nearby chaotic saddle in an…
A nonsmooth fold is where an equilibrium or limit cycle of a nonsmooth dynamical system hits a switching manifold and collides and annihilates with another solution of the same type. We show that beyond the bifurcation the leading-order…
In this paper, we consider a smooth arc of diffeomorphisms which has a saddle-node bifurcation inside a nontrivial invariant set which is a deformation of a horseshoe. We show that this saddle-node bifurcation is isolated, that is, its…
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…
A transition from a smooth torus to a chaotic attractor in quasiperiodically forced dissipative systems may occur after a finite number of torus-doubling bifurcations. In this paper we investigate the underlying bifurcational mechanism…
Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical…
Strange nonchaotic attractors (SNAs) have been identified and studied in the literature exclusively in quasiperiodically driven nonlinear dynamical systems. It is an interesting question to ask whether they can be identified with other…
Strange nonchaotic attractors (SNAs) can be created due to the collision of an invariant curve with itself. This novel ``homoclinic'' transition to SNAs occurs in quasiperiodically driven maps which derive from the discrete Schr\"odinger…
We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…