Related papers: Testing Critical Slowing Down as a Bifurcation Ind…
We study elastic snap-through induced by a control parameter that evolves dynamically. In particular, we study an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening…
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…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node…
We study a dynamical counterpart of bifurcation to invariant torus for a system of interconnected fast phase variables and slowly varying parameters. We show that in such a system, due to the slow evolution of parameters, there arise…
The slow passage through a Hopf bifurcation leads to the delayed appearance of large amplitude oscillations. We construct a smooth scalar feedback control which suppresses the delay and causes the system to follow a stable equilibrium…
Anticipating bifurcation-induced transitions in dynamical systems has gained relevance in various fields of the natural, social, and economic sciences. Before the annihilation of a system's equilibrium point by means of a bifurcation, the…
We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…
A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…
A singularly perturbed system for doubly diffusive convection equations, called the artificial compressible system, is considered on a two-dimensional infinite layer for a parameters range where the Hopf bifurcation occurs in the…
Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of control parameter greatly affects the performance of early…
Critical slowing down (CSD) has been a trademark of critical dynamics for equilibrium phase transitions of a many-body system, where the relaxation time for the system to reach thermal equilibrium or quantum ground state diverges with…
This paper studies bifurcations in a three node power system when excitation limits are considered. This is done by approximating the limiter by a smooth function to facilitate bifurcation analysis. Spectacular qualitative changes in the…
We consider second-order phase transitions in which the order parameter is a replicated overlap matrix. We focus on a tricritical point that occurs in a variety of mean-field models and that, more generically, describes higher order…
We study signatures of critical behavior in microscopic simulations of small, highly excited Lennard-Jones drops. We focus our attention on the behavior of the system at the time of fragment formation (which takes place in phase space) and…
Static and dynamic properties of two-dimensional bidisperse dissipative particles are numerically studied near the jamming transition. We investigate the dependency of the critical scaling on the ratio of the different diameters and find a…
Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small…
This paper shows that the variance of load bus voltage magnitude in a small power system test case increases monotonically as the system approaches a Hopf bifurcation. This property can potentially be used as a method for monitoring…