Related papers: Limit Processes and Bifurcation Theory of Quasi-Di…
An autonomous system of ordinary differential equations in the plane with a centre-saddle bifurcation is considered. The influence of time damped perturbations with power-law asymptotics is investigated. The particular solutions tending at…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We…
For characterizing the Brownian motion in a bounded domain: $\Omega$, it is well-known that the boundary conditions of the classical diffusion equation just rely on the given information of the solution along the boundary of a domain; on…
We study perturbation theory in certain quantum mechanics problems in which the perturbing potential diverges at some points, even though the energy eigenvalues are smooth functions of the coefficient of the potential. We discuss some of…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…
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…
We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when…
Currently, there is no general theory for deriving diffusion approximations of queueing systems with high- or infinite-dimensional state descriptors. In this paper, we explore one path for deriving diffusion limit equations of queueing…
We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…
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…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
We study the dynamics of fluctuations at the critical point for two time-asymmetric version of the Curie-Weiss model for spin systems that, in the macroscopic limit, undergo a Hopf bifurcation. The fluctuations around the macroscopic limit…
We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove bifurcation of limit cycles from focus boundary equilibria in other types of…
We consider diffusion processes in media with pockets of large diffusivity. The asymptotic behavior of such processes is described when the diffusion coefficients in the pockets tend to infinity. The limiting process is identified as a…