periodic orbit
1 Follower
Recent papers in periodic orbit
Abstract: A weakly nonlinear third-order equation describing the behavior of the phase of the electric field of a single-mode semiconductor laser subject to optical injection and detuning is analyzed. The method of averaging is used to... more
Abstract: We use a third-order phase equation associated with the Maxwell-Bloch equations to investigate the behavior of a single-mode semiconductor laser subject to injection and frequency detuning. The weakly nonlinear phase equa-tion... more
We extend the temporal spectral element method further to study the periodic orbits of general autonomous nonlinear delay differential equations (DDEs) with one constant delay. Although we describe the approach for one delay to keep the... more
In a previous paper, the author introduced a Floer-theoretic torsion invariant I_F, which roughly takes the form of a product of a power series counting perturbed pseudo-holomorphic tori, and the Reidemeister torsion of the symplectic... more
This thesis is a collection of studies on coupled nonconservative oscillator systems which contain an oscillator with parametric excitation. The emphasis this study will, on the one hand, be on the bifurcations of the simple solutions... more
We discuss new and improved algorithms for the bifurcation analysis of fixed points and periodic orbits (cycles) of maps and their implementation in matcont, a matlab toolbox for continuation and bifurcation analysis of dynamical systems.... more
We study the streamlines of the velocity field produced by two unlinked vortex rings. We find that two vortex rings can produce chaos and observe a route to chaos directly from periodic orbits. From the case study of numerous ring... more
In this work we consider a 1:− 1 non-semi-simple resonant periodic orbit of a three degrees of freedom real analytic Hamiltonian system. From the formal analysis of the normal form, we prove the branching off of a two-parameter family of... more
Using semi-classical formalism and asymptotic proliferation law of periodic orbits, we obtain an analytical expressions for the two-level cluster function, spectral form factor, level spacing distribution and the number variance for... more
A simple discrete planar dynamical model for the ideal (logical) R–S flip-flop circuit is developed with an eye toward mimicking the dynamical behavior observed for actual physical realizations of this circuit. It is shown that the model... more
We show that in the neighborhood of the tripling bifurcation of a periodic orbit of a Hamiltonian flow or of a fixed point of an area preserving map, there is generically a bifurcation that creates a ``twistless'' torus. At this... more
Riddled basins denote a characteristic type of fractal domain of attraction that can arise when a chaotic motion is restricted to an invariant subspace of total phase space. An example is the synchronized motion of two identical chaotic... more