Related papers: Nonautonomous saddle-node bifurcations: random and…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
Concave in measure and d-concave in measure nonautonomous scalar ordinary differential equations given by coercive and time-compactible maps have similar properties to equations satisfying considerably more restrictive hypotheses. This…
Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov…
We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…
We explore different families of quasi-periodically Forced Logistic Maps for the existence of universality and self-similarity properties. In the bifurcation diagram of the Logistic Map it is well known that there exist parameter values…
The saddle-node bifurcation on an invariant circle (SNIC) is one of the codimension-one routes to creation or destruction of a periodic orbit in a continuous-time dynamical system. It governs the transition from resting behaviour to…
We demonstrate that scale-free patterns are observed in a spatially extended stochastic system whose deterministic part undergoes a saddle-node bifurcation. Remarkably, the scale-free patterns appear only at a particular time in relaxation…
A common external forcing can cause a saddle-node bifurcation in an ensemble of identical Duffing oscillators by breaking the symmetry of the individual bistable (double-well) unit. The strength of the forcing determines the separation…
Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a…
We study the dynamics of the Forced Logistic Map in the cylinder. We compute a bifurcation diagram in terms of the dynamics of the attracting set. Different properties of the attracting set are considered, as the Lyapunov exponent and, in…
We study bifurcations of invariant graphs in skew product dynamical systems driven by hyperbolic surface maps T like Anosov surface diffeomorphisms or baker maps and with one-dimensional concave fibre maps under multiplicative forcing when…
There is growing interest in anticipating critical transitions in natural systems, often pursued through statistical detection of early warning signals associated with dynamical bifurcations. In stochastic dynamical systems, such signals…
From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal,…
We consider the effect on tipping from an additive periodic forcing in a canonical model with a saddle node bifurcation and a slowly varying bifurcation parameter. Here tipping refers to the dramatic change in dynamical behavior…
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.…
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…
We propose a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism is first discussed on an heuristic level and by means of…
Sidorenko's conjecture states that the number of copies of any given bipartite graph in another graph of given density is asymptotically minimized by a random graph. The forcing conjecture further strengthens this, claiming that any…
We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of…
This work provides a geometric approach to the study of bifurcation and rate induced transitions in a class of non-autonomous systems referred to herein as $\textit{asymptotically slow-fast systems}$, which may be viewed as 'intermediate'…