Related papers: Variance-based control of regime shifts: bistabili…
In the wake of the SARS-CoV-2 pandemic, there has been heightened interest from applied mathematicians in infectious disease modelling. Modelling efforts often focus on predicting whether diseases are likely to be eliminated or, instead,…
Successfully anticipating sudden major changes in complex systems is a practical concern. Such complex systems often form a heterogeneous network, which may show multistage transitions in which some nodes experience a regime shift earlier…
In this topical review, we present a brief overview of the different methods and measures to detect the occurrence of critical transitions in complex systems. We start by introducing the mechanisms that trigger critical transitions, and how…
Developing methods for detecting tipping phenomena at an early stage is an important problem in various fields such as ecology, medicine, and economics. A tipping phenomenon is characterized by a rapid transition resulting from the…
Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress…
The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from…
In a nonautonomous nonlinear dynamical system, generic critical transitions (tipping points) are not limited to slow passage through fold bifurcations. They can also correspond to slow passage through other generic bifurcations, such as…
Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to…
Real-life systems often experience regime shifts. An early warning signal (EWS) is a quantity that attempts to anticipate such a regime shift. Because complex systems of practical interest showing regime shifts are often dynamics on…
The existence of persistent midlatitude atmospheric flow regimes with time-scales larger than 5-10 days and indications of preferred transitions between them motivates to develop early warning indicators for such regime transitions. In this…
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…
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…
Identifying the instances of jumps in a discrete-time-series sample of a jump diffusion model is a challenging task. We have developed a novel statistical technique for jump detection and volatility estimation in a return time series data…
Real power systems exhibit dynamics that evolve across a wide range of time scales, from very fast to very slow phenomena. Historically, incorporating these wide-ranging dynamics into a single model has been impractical. As a result, power…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…
In this paper, we study the applicability of an early warning index while studying the transitions to complete and generalized synchronizations in the coupled oscillator models using an unconventional system parameter and the coupling…
Prior research has shown that autocorrelation and variance in voltage measurements tend to increase as power systems approach instability. This paper seeks to identify the conditions under which these statistical indicators provide reliable…
Bifurcations in dynamical systems characterize qualitative changes in the system behavior. Therefore, their detection is important because they can signal the transition from normal system operation to imminent failure. While standard…