Related papers: A simple criterion for identifying slow-fast relax…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
A general kind of models with hierarchically constrained dynamics is shown to exhibit logarithmic anomalous relaxation, similarly to a variety of complex strongly interacting materials. The logarithmic behavior describes most of the decay…
An ultra-strong coupling regime takes place in a compound system when a coupling strength between the subsystems exceeds one tenth of the system eigenfrequency. It transforms into a deep-strong coupling regime when the coupling strength…
The relaxation oscillations of Zeeman and dipole magnetizaions in spin system of a solid paramagnet are theoretically analyzed under conditions of intermediate saturation of magnetic resonance and strong low-frequency modulation of the…
The paper presents a complete study of simple homoclinic cycles in R^5. We find all symmetry groups Gamma such that a Gamma-equivariant dynamical system in R^5 can possess a simple homoclinic cycle. We introduce a classification of simple…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
We prove that the equilibrium fluctuations of the symmetric simple exclusion process in contact with slow boundaries is given by an Ornstein-Uhlenbeck process with Dirichlet, Robin or Neumann boundary conditions depending on the range of…
New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…
We study the relaxation dynamics of systems of straight, parallel crystal dislocations, starting from initially random and uncorrelated positions of the individual dislocations. A scaling model of the relaxation process is constructed by…
Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…
Oscillatory behavior is a key property of many biological systems. The Small-Gain Theorem (SGT) for input/output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium and hence its violation is a…
We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…