相关论文: High order amplitude equation for steps on creep c…

We consider a model proposed earlier by us for describing a form of plastic instability found in creep experiments . The model consists of three types of dislocations and some transformations between them. The model is known to reproduce a…

For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…

Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that…

Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…

We investigate the KdV-Burgers and Gardner equations with dissipation and external perturbation terms by the approach of dynamical systems and Shil'nikov's analysis. The stability of the equilibrium point is considered, and Hopf…

The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…

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…

Hopf bifurcations have been studied perturbatively under two broad headings, viz., super-critical and sub-critical. The criteria for occurrences of such bifurcations have been investigated using the renormalization group. The procedure has…

We study the weakly nonlinear saturation of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. This instability, established in our preceding work as a Hopf bifurcation of a…

A four-dimensional mathematical model of the hypothalamus-pituitary-adrenal (HPA) axis is investigated, incorporating the influence of the GR concentration and general feedback functions. The inclusion of distributed time delays provides a…

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing…

Propagation of uncertainty in dynamical systems is a significant challenge. Here we focus on random multiscale ordinary differential equation models. In particular, we study Hopf bifurcation in the fast subsystem for random initial…

Dynamical properties of ultradiscrete Hopf bifurcation, similar to those of the standard Hopf bifurcation, are discussed by proposing a simple model of ultradiscrete equations with max-plus algebra. In ultradiscrete Hopf bifurcation, limit…

Hydrodynamic instabilities often cause spatio-temporal pattern formations and transitions between them. We investigate a model experimental system, a density oscillator, where the bifurcation from a resting state to an oscillatory state is…

Since the seminal work by H.L.F. Helmholtz in 1863, to understand the basic principles of hearing has been a great, but still unresolved, challenge for physicists. Some time ago, it has been pointed out (Egu\'{\i}luz et al., Phys. Rev.…

Nonlinear normal modes are periodic orbits that survive in nonlinear many-body Hamiltonian systems, and their instability is crucial for relaxation dynamics. Here, we study the instability process of the $\pi/3$-mode in the…

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.

The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…

In order to investigate the emergence of periodic oscillations of rimming flows, we study analytically the stability of steady states for the model of (Benilov, Kopteva, O'Brien, 2005), which describes the dynamics of a thin fluid film…

For piecewise-smooth ordinary differential equations, the occurrence of a Hopf bifurcation on a switching surface is known as a boundary Hopf bifurcation. Boundary Hopf bifurcations are codimension-two, so occur at points in two-parameter…