Related papers: Bifurcation and Stability of Two-Dimensional Doubl…
We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the…
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
The fundamental mechanism of hysteresis in the quasistatic limit of multi-stable systems is associated with transitions of the system from one local minimum of the potential energy to another. In this scenario, as system parameters are…
This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.
We investigate the non-linear dynamics of a two-dimensional film flowing down a finite heater, for a non-volatile and a volatile liquid. An oscillatory instability is predicted beyond a critical value of Marangoni number using linear…
Steady states of the Swift--Hohenberg equation are studied. For the associated four--dimensional ODE we prove that on the energy level $E=0$ two smooth branches of even periodic solutions are created through the saddle-node bifurcation. We…
In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation…
We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area…
We investigate the universality in collisionless nonlinear dynamics of a codimension-two bifurcation where two eigenvalues collide at the origin, and two lines of continuous bifurcation and discontinuous jump meet. Through linear analysis…
Instability patterns of rolling up a sleeve appear more intricate than the ones of walking over a rug on floor, both characterized as uniaxially compressed soft-film/stiff-substrate systems. This can be explained by curvature effects. To…
We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we…
Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…
Bifurcations associated with stability of the saddle fixed point of the Poincar\'{e} map, arising from the unstable equilibrium point of the potential, are investigated in a forced Duffing oscillator with a double-well potential. One…
Let us give a two dimensional family of real vector fields. We suppose that there exists a stationary point where the linearized vector field has successively a stable focus, an unstable focus and an unstable node. When the parameter moves…
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…
Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating spherical shell can exhibit a rather large number of behaviours often distinct from that of the single diffusive system. In order to understand how…
A sequence of three steady - oscillatory transitions of buoyancy convection of air in a laterally heated cube with perfectly thermally insulated horizontal and spanwise boundaries is studied. The problem is treated by Newton and Arnoldi…
We study the convective patterns that arise in a nearly semi-cylindrical cavity fed in with hot fluid at the upper boundary, bounded by a cold, porous semi-circular boundary at the bottom, and infinitely extended in the third direction.…