A new fully numerical method is presented which employs multiple Poincaré sections to find quasi-periodic orbits. The main advantages of this method are the small overhead cost of programming and very fast execution times, robust behavior near chaotic regions that leads to full convergence for given family of quasi-periodic orbits and the minimal memory required to store these orbits. This meth...

In this study, an octagonal-based self-organizing network’s lattice structure is proposed to allow more exploration and exploitation in updating the weights for better mapping and classification performances. The neighborhood of the octagonal-based lattice structure provides more nodes for the weights updating than standard hexagonal-based lattice structure. Based on our experiment, the octagon...

Periodicity and aperiodicity can exist in a state simultaneously typically become quasi-periodicity quasi-aperiodicity dynamically changing state. The quasi-periodic quasi-aperiodic states existing the periodic/aperiodic mostly correspond to different phenomena require controls. For separation control of these states, this paper defines periodic/aperiodic, quasi-periodic, construct filter that ...

By exploiting a recently developed connection between Heun’s differential equation and the generalized associated Lamé equation, we not only recover the well known periodic solutions, but also obtain a large class of new, quasi-periodic solutions of Heun’s equation. Each of the quasi-periodic solutions is doubly degenerate.

We consider 1-D quasi-periodic Frenkel-Kontorova models (describing, for example, deposition of materials in a quasi-periodic substratum). We study the existence of equilibria whose frequency (i.e. the inverse of the density of deposited material) is resonant with the frequencies of the substratum. We study perturbation theory for small potential. We show that there are perturbative expansions ...

In this note, the present author’s recent works on nonlinear wave equations via KAM theory are introduced and reviewed. The existence of solutions, periodic in time, for non-linear wave (NLW) equations has been studied by many authors. A wide variety of methods such as bifurcation theory and variational techniques have been brought on this problem. See [11] and the references therein, for examp...

In order to investigate the effects of non-linear springs in vibrating behavior of vehicles, the independent suspension of conventional vehicles could be modeled as a non-linear single degree of freedom system. The equation of motion for the system would be a non-linear third order ordinary differential equation, when considering the elasticity of rubber bushings in joints of shock absorber. It...