Related papers: Rate-induced Tipping in Discrete-time Dynamical Sy…
In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…
Many physical systems are forced by external inputs, which can sometimes take the form of chaotic variation. A particular example is found in applications related to weather and climate, where chaotic variation is prevalent across various…
A variation in the environment of a system, such as the temperature, the concentration of a chemical solution or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point,…
Previous studies have shown that rate-induced transitions can occur in pullback attractors of systems subject to "parameter shifts" between two asymptotically steady values of a system parameter. For cases where the attractors limit to…
An in-depth analysis of nonautonomous bifurcations of saddle-node type for scalar differential equations $x'=-x^2+q(t)\,x+p(t)$, where $q\colon\mathbb{R}\to\mathbb{R}$ and $p\colon\mathbb{R}\to\mathbb{R}$ are bounded and uniformly…
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…
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…
We propose an approximation for the probability of tipping when the speed of parameter change and additive white noise interact to cause tipping. Our approximation is valid for small to moderate drift speeds and helps to estimate the…
Recent progress in randomized motion planners has led to the development of a new class of sampling-based algorithms that provide asymptotic optimality guarantees, notably the RRT* and the PRM* algorithms. Careful analysis reveals that the…
We prove that return time statistics of a dynamical system do not change if one passes to an induced (i.e. first return) map. We apply this to show exponential return time statistics in i) smooth interval maps with nowhere-dense critical…
Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…
We propose a framework to study tipping points in reaction-diffusion equations (RDEs) in one spatial dimension, where the reaction term decays in space (asymptotically homogeneous) and varies linearly with time (nonautonomous) due to an…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
A habitat that is moving due to environmental change may result in tipping to extinction if the rate at which it moves is too great. We use a scalar reaction-diffusion equation with a non-autonomous reaction term, representing a spatially…
A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals…
We provide a unified analytic approach to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical systems and random attractors. Part I deals with driving paths of finite…
The early detection of tipping points, which describe a rapid departure from a stable state, is an important theoretical and practical challenge. Tipping points are most commonly associated with the disappearance of steady-state or periodic…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…