Related papers: Dynamical behavior of a system modeling wave bifur…
This paper investigates the stability and bifurcation of the two-dimensional viscous primitive equations with full diffusion under thermal forcing. The system governs perturbations about a motionless basic state with a linear temperature…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
Motivated by the study of conditional stability of traveling waves, we give an elementary $H^2$ center stable manifold construction for quasilinear parabolic PDE, sidestepping apparently delicate regularity issues by the combination of a…
The dynamics of a model, originally proposed for a type of instability in plastic flow, has been investigated in detail. The bifurcation portrait of the system in two physically relevant parameters exhibits a rich variety of dynamical…
In this paper we develop hydrodynamic models using spectral differential operators to investigate the spatial stability of swirling fluid systems. Including viscosity as a valid parameter of the fluid, the hydrodynamic model is derived…
The oscillation model, based on the wave equation on networks, can describe user dynamics in online social networks. The fundamental equation of user dynamics can be introduced into the oscillation model to explicitly describe the causal…
Particles suspended in fluid flow through a curved duct focus to stable equilibrium positions in the duct cross-section due to the balance of two dominant forces: (i) inertial lift force - arising from the inertia of the fluid, and (ii)…
We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic…
Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and…
Motivated by recent analytical and numerical work on two- and three-dimensional convection with imposed spatial periodicity, we analyse three examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic…
In this paper, we derive consistent shallow water equations for bi-layer flows of Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency regime and show the occurence of…
This work investigates the emergence of oscillations in one of the simplest cellular signaling networks exhibiting oscillations, namely, the dual-site phosphorylation and dephosphorylation network (futile cycle), in which the mechanism for…
We study a new discrete-time dynamical system on circle patterns with the combinatorics of the square grid. This dynamics, called Miquel dynamics, relies on Miquel's six circles theorem. We provide a coordinatization of the appropriate…
We study the bifurcation of periodic travelling waves of the capillary-gravity Whitham equation. This is a nonlinear pseudo-differential equation that combines the canonical shallow water nonlinearity with the exact (unidirectional)…
We examine examples of weakly nonlinear systems whose steady states undergo a bifurcation with increasing forcing, such that a forced subsystem abruptly ceases to absorb additional energy, instead diverting it into an initially quiescent,…
Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making…
An understanding of the dynamics of differentially rotating systems is key to many areas of astrophysics. We investigate the oscillations of a simple system exhibiting differential rotation, and discuss issues concerning the role of…
We study the principal bifurcation curve of a third order equation which describes the nonlinear evolution of several systems with a long--wavelength instability. We show that the main bifurcation branch can be derived from a variational…
We study the spectrum of the linearization around standing wave profiles for two quantum hydrodynamics systems with linear and nonlinear viscosity. The essential spectrum for such profiles is stable; we investigate the point spectrum using…
To ease analysis and simulation we make low-dimensional models of complicated dynamical systems. Centre manifold theory provides a systematic basis for the reduction of dimensionality from some detailed dynamical prescription down to a…