Many interesting models in science and engineering involve forced or coupled oscillators. The most striking feature of such systems is the transition between phase locking and quasi-periodicity. Phase locking produces a periodic solution that generically persists under variation of parameters. In contrast, quasi-periodicity is a codimension-one phenomenon, which is thus generically destroyed by...

We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem −∆u = λf(x) (1−u)2 on a bounded domain Ω ⊂ R , which models –among other things– a simple electrostatic Micro-Electromechanical System (MEMS) device. We extend the results of [11] relating to the minimal branch, by obtaining compactness along unstable ...

The solar-wind-driven magnetosphere–ionosphere exhibits a variety of dynamical states including low-level steady plasma convection, episodic releases of geotail stored plasma energy into the ionospheric known broadly as substorms, and states of continuous strong unloading. The WINDMI model @J. P. Smith et al., J. Geophys. Res. 105, 12 983 ~2000!# is a six-dimensional substorm model that uses a ...

In this work we consider the Colpitts oscillator as a paradigm for sinusoidal oscillation and we investigate its nonlinear dynamics. In particular, we carry out a two-parameter bifurcation analysis of a model of the oscillator. This analysis is conducted by combining numerical continuation techniques and normal form theory. First, we show that the birth of the harmonic cycle is associated with ...

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing t...

As a nonlinear memory device, the memristor is often used as circuit load. In this paper, system based on traditional current-mode Cuk converter with voltage-controlled constructed. By deducing state equation of topology and continuous current mode equation, simulation model The dynamic characteristics are explored by using sequence diagram, phase diagram bifurcation diagram. addition, parametr...

We study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady-state solutions, and their stability. By employing a variational approach for a quasi-one-dimensional, two-atomic species condensate, we obtain equations of motion for the parameters of each species: amplitude, widt...

In this paper, several three dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have a number of similar features. A new 3-D continuous autonomous system is proposed based on these features. The new system can generate a four-wing chaotic attractor with less terms in the system equations. Several basic properties of the new syste...