相关论文: Rate-induced tipping and saddle-node bifurcation f…

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 consider how breakdown of the quasistatic approximation for attractors can lead to rate-induced tipping, where a qualitative change in tracking/tipping behaviour of trajectories can be characterised in terms of a critical rate.…

We present a novel exactly solvable ordinary differential equation model for rate-induced tipping: a dynamic phenomenon of dynamical systems where a time-dependent parameter triggers the transition of stability of a system. Our model…

A dynamical system is said to undergo rate-induced tipping when it fails to track its quasi-equilibrium state due to an above-critical-rate change of system parameters. We study a prototypical model for rate-induced tipping, the saddle-node…

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…

The current definition of rate-induced tipping is tied to the idea of a pullback attractor limiting in forward and backward time to a stable quasi-static equilibrium. Here we propose a new definition that encompasses the standard definition…

When parameters of a dynamical system change sufficiently fast, critical transitions can take place even in the absence of bifurcations. This phenomenon is known as rate-induced tipping and has been reported in a variety of systems, from…

Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced…

We analyze rate-dependent tipping in a fast/slow system with an equilibrium near the fold of a critical manifiold. We find a Hopf bifurcation as the rate parameter increases in the reduced co-moving system. This implies the growth of a…

A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In mathematical models, tipping can be caused by bifurcations,…

The paper deals with the study of rate-induced tipping in asymptotically autonomous scalar ordinary differential equations. We prove that, in such a tipping scenario, a solution which limits at a hyperbolic stable equilibrium of the past…

There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered…

We develop a definition of rate-induced tipping (R-tipping) in discrete-time dynamical systems (maps) and prove results giving conditions under which R-tipping will or will not happen. Specifically, we study (possibly non-invertible) maps…

We discuss tipping phenomena (critical transitions) in nonautonomous systems using an example of a bistable ecosystem model with environmental changes represented by time-varying parameters [Scheffer et al., Ecosystems, 11 (2008), pp.…

A function with finite asymptotic limits gives rise to a transition equation between a "past system" and a "future system". This question is analyzed in the case of nonautonomous coercive nonlinear scalar ordinary differential equations…

Rate-induced tipping is an instability that occurs in a system when its time-dependent rate parameter becomes larger than a threshold value. We investigate a Pearson diffusion process, a diffusion process having solutions staying in a…

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,…

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…

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…