The forces acting on an isotropic microsphere in optical tweezers are effectively conservative. However, reductions the symmetry of particle or trapping field can break this condition. Here we theoretically analyze motion a linearly nonconservative vacuum trap, concentrating case where is broken by birefringence, causing coupling between rotational and translational degrees freedom. Neglecting ...

Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent a...

This paper concerns the control design of a PID controlled gimbals suspension gyro, whose parameters are determined by using bifurcation theory. The non-linear mathematical model of the gyro is deduced by using the nutation theory of gyroscopes. Considering a PID controller with constrained integral action, it is shown that depending on different values of the maximum allowed integral action a ...

In this paper, dynamical systems theory and bifurcation theory are applied to investigate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous investigations of epidemiology, in-host disease, and autoimmunity. These closely related models display interesting dynamical behaviors including bistability, recurr...

Recent investigations on the bifurcation behavior of power electronic dc-dc converters has revealed that most of the observed bifurcations do not belong to generic classes like saddle-node, period doubling or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a xed point crosses the \border" betw...

We investigate the destabilization mechanisms of dissipative solitons in inhomogeneous nonlinear resonators subjected to injection and time-delayed feedback. consider paradigmatic Lugiato-Lefever model describing driven optical resonator. analyze pinning-depinning transition by introducing a potential induced inhomogeneity. Further, we identify conditions under which these structures are destab...

We consider diierential equations _ x = f (x;) where the parameter = "t moves slowly through a bifurcation point of f. Such a dynamic bifurcation is often accompanied by a possibly dangerous jump transition. We construct smooth scalar feedback controls which avoid these jumps. For transcritical and pitchfork bifurcations, a small constant additive control is usually suucient. For Hopf bifurcati...

We study the solutions of a system of three coupled excitable cells with D3 symmetry. The system has two parameters, one controls the local dynamics of each cell and the other the strength of the coupling. We find and describe self-sustained collective oscillations. Periodic solutions appear in global bifurcations, typically after the collapse of fixed points heteroclinically connected. The sym...

This paper studies various Hopf bifurcations in the two-dimensional plane Poiseuille problem. For several values of the wavenumber α, we obtain the branch of periodic flows which are born at the Hopf bifurcation of the laminar flow. It is known that, taking α ≈ 1, the branch of periodic solutions has several Hopf bifurcations to quasi-periodic orbits. For the first bifurcation, previous calcula...

In this paper, we study Hopf-zero bifurcation in a generalized Gopalsamy neural network model. By using multiple time scales and center manifold reduction methods, we obtain the normal forms near a Hopf-zero critical point. A comparison between these two methods shows that the two normal forms are equivalent. Moreover, bifurcations are classified in two-dimensional parameter space near the crit...