Related papers: Tipping in complex systems under fast variations o…

Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the…

Planar switched system with dead-zone are analyzed. In particular, we consider the effects of perturbation of the linear control law from purely positional to position-velocity control. This type of perturbation leads to a novel Hopf-like…

The amplitude equation of Gierer-Mainhardt model has been actually derived near the boundary abuot which Turing and Hopf modes exist. In a parameter region where Hopf-Turing mixed mode solution is stable, a chaotic state that generally…

The behavior of a stationary inverted point mass pendulum pivoted at its lower end in a gravitational potential is studied under the influence of statistical fluctuations. It is shown using purely classical equations that the pendulum…

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…

Nonsmooth formulations of physical models are common, particularly in climate modeling. However, in many of these models, there is little justification for this modeling choice, and no mathematical indication that the resulting behavior in…

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…

Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…

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 networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients…

Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…

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…

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…

Abrupt transitions are a central concern in climate and ecological research, and may arise when critical thresholds known as tipping points are crossed. However, previous work has shown that finite-time overshoots of tipping points can be…

In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…

We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a…

Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is…

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…

Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling. This behavior can naturally emerge in tricritical systems on heterogeneous networks and it is strongly enhanced by the…

Polyhomeostatic adaption occurs when evolving systems try to achieve a target distribution function for certain dynamical parameters, a generalization of the notion of homeostasis. Here we consider a single rate encoding leaky integrator…