Related papers: Trapping Phenomenon Attenuates Tipping Points for …
Tipping points are critical thresholds of parameters where tiny perturbations can lead to abrupt and large qualitative changes in the systems. Many real-world systems that exhibit tipping behavior can be represented as networks of…
Regime shifts are quite common in complex systems like cell regulations, disease transmissions, ecosystems, marine ice instability, etc. Several statistical indicators known as early warning signals (EWS) have been theorized to anticipate…
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the…
Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements…
Elastic strips provide a canonical system for studying the mechanisms governing elastic shape transitions. Buckling, linear snap-through, and nonlinear snap-through have been observed in boundary-actuated strips and linked to the type of…
Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…
A dynamical system that undergoes a supercritical Hopf's bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter $\epsilon$. The random fluctuations of the system at the critical point are studied…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
We explore the critical properties of the recently discovered finite-time dynamical phase transition in the non-equilibrium relaxation of Ising magnets after a temperature quench. The transition is characterized by a sudden switch in the…
For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
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…
A phase transition is an example of a ``topological defect'' in the space of parameters of a quantum or classical many-body systems. In this paper, we consider phase diagram topological defects of higher codimension. These have the property…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
We present a phenomenological description of the critical slowing down associated with period-doubling bifurcations in discrete dynamical systems. Starting from a local Taylor expansion around the fixed point and the bifurcation parameter,…
The use of critical slowing down as an early warning indicator for regime switching in observations from stochastic environments and noisy dynamical models has been widely studied and implemented in recent years. Some systems, however, have…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
The manipulation of the self-organized critical systems by repeatedly deliberate local relaxations (fillips) affect considerably the dynamics of avalanches and change their evolution. During a fillip, the energy diffuses to the neighboring…