Related papers: Nonlinear dynamic interactions between flow-induce…
In this paper, we consider the unfolding of the real-analytic and generic zero-Hopf bifurcation of co-dimension two. It is well-known that in an open set of parameter space the splitting of one-dimensional stable and unstable manifolds is…
We study the aerodynamic response of a pre-stressed curved aileron. Whilst the fluid flow is standard (high Reynolds air flow undisturbed at infinity), the structure is designed to have a peculiar nonlinear behavior. Specifically, the…
Nonlinear behavior in the hopping transport of interacting charges enables reconfigurable logic in disordered dopant network devices, where voltages applied at control electrodes tune the relation between voltages applied at input…
Spatiotemporal localized and extended structures associated with a subcritical finite wavenumber Hopf bifurcation are studied in the Purwins model (a three-variable FitzHugh-Nagumo version). Steady and time-dependent numerical continuation…
We consider analytically and numerically head-on collision between two self-propelled drops. Each drop is driven by chemical reactions that produce or consume the concentration isotropically. The isotropic distribution of the concentration…
For the reduced two-dimensional Belousov-Zhabotinsky slow-fast differential system, the known results are the existence of one limit cycle and its stability for particular values of the parameters. Here, we characterize all dynamics of this…
The cavitation of solid elastic spheres is a classical problem of continuum mechanics. Here, we study this problem within the context of "stochastic elasticity" where the constitutive parameters are characterised by probability density…
This work studies front formation in the Allen-Cahn equation with a parameter heterogeneity which slowly varies in space. In particular, we consider a heterogeneity which mediates the local stability of the zero state and subsequent…
The population dynamics in a modified Leslie-Gower model with an additive Allee effect are highly sensitive to both parameters and initial population densities, leading to outcomes ranging from coextinction to sustained multistable steady…
In this paper we analyze the heteroclinic cycle and the Hopf bifurcation of a generic dynamical system with the symmetry of the group $\mathbf{Q}_8,$ constructed via a Cayley graph. While the Hopf bifurcation is similar to that of a…
Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing…
We present a framework for analyzing collections of interacting hysterons through the lens of catastrophe theory. By modeling hysteron dynamics as a gradient system, we show how to construct hysteron transition graphs by characterizing the…
When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order "guiding system", placing the time dependence at higher orders. Recent research focused on…
This paper presents a numerical analysis of the transition from selective withdrawal to viscous entrainment. In our model problem, an interface between two immiscible layers of equal viscosity is deformed by an axisymmetric withdrawal flow,…
Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in fluid networks containing either multiple phases or constituent flows. In many systems, such behavior might be attributed to the complicated…
We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…
The equivariant Hopf bifurcation dynamics of a class of system of partial differential equations is carefully studied. The connections between the current dynamics and fundamental concepts in hyperbolic conservation laws are explained. The…
Recently, it has been shown that properties of excitable media stirred by two-dimensional chaotic flows can be properly studied in a one-dimensional framework \cite{excitablePRL,excitablePRE}, describing the transverse profile of the…
We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a contact line. This is a main challenge in numerical simulations of two-phase flows with moving contact lines. We derive a two-dimensional…