Related papers: Attractor Bifurcation of Three-Dimensional Double-…
The global bifurcation diagrams for two different one-parametric perturbations ($+\lambda x$ and $+\lambda x^2$) of a dissipative scalar nonautonomous ordinary differential equation $x'=f(t,x)$ are described assuming that 0 is a constant…
Onset of double-component convection due to different boundary conditions is studied in a diversely oriented infinite slot with broken reflection symmetry between the slot conditions for a component. Among other outcomes, the broken…
The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…
A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The…
We construct global curves of rotational traveling wave solutions to the $2D$ water wave equations on a compact domain. The real analytic interface is subject to surface tension, while gravitational effects are ignored. In contrast to the…
A diffusive ratio-dependent Holling-Tanner system subject to Neumann boundary conditions is considered. The existence of multiple bifurcations, including Turing-Hopf bifurcation, Turing-Truing bifurcation, Hopf-double-Turing bifurcation and…
Doubly diffusive convection describes the fluid motion driven by the competition of temperature and salinity gradients diffusing at different rates. While the convective motions driven by these gradients usually occupy the entire domain,…
We recently described a specific type of attractors of two-dimensional discontinuous piecewise linear maps, characterized by two discontinuity lines dividing the phase plane into three partitions, related to economic applications. To our…
A two-fluid model is proposed to describe the transport properties of granular superconductors. Using the resistively shunted junction model and some aspects of the two-level system theory, a statistical model is developed which takes into…
We study a class of 2-dimensional Hamiltonian systems $H(x,y,p_x,p_y)=\frac12(p_x^2+p_y^2) +V(x,y)$ in which the plane $x$=$p_x$=0 is invariant under the Hamiltonian flow, so that straight-line librations along the y axis exist, and we also…
This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle $\gamma$ and the Rayleigh number $R$.…
The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
The analysis of vibration effect on non-isothermal fluid in closed cavity is important for planning technological experiments in space. Control and optimization of these processes critically depend on the understanding of liquid response to…
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the…
The linear eigenvalue problem governing the stability of the mechanical equilibrium of the fluid in a electrohydrodynamic (EHD) convection problem is investigated. The analytical study is one of bifurcation. This allows us to regain the…
The formulation of the variational problems for the solute transport in a fluid layer in presence of double-diffusive thermal convection is discussed. It is shown that the variational functional obtained by Strauss can be generalized and…
Convection in horizontal layers of binary fluids heated from below and in particular the influence of the Soret effect on the bifurcation properties of extended stationary and traveling patterns that occur for negative Soret coupling is…
A codimension-three bifurcation, characterized by a pair of purely imaginary eigenvalues and a nonsemisimple double zero eigenvalue, arises in the study of a pair of weakly coupled nonlinear oscillators with Z_2 + Z_2 symmetry. The…
In this paper we study continuous parametrized families of dissipative flows, which are those flows having a global attractor. The main motivation for this study comes from the observation that, in general, global attractors are not robust,…