Different routes to chaos via strange nonchaotic attractor in a quasiperiodically forced system

This paper focusses attention on the strange nonchaotic attractors (SNA) of a quasiperiodically forced dynamical system. Several routes, including the standard ones by which the appearance of strange nonchaotic attractors takes place, are shown to be realizable in the same model over a two parameters ($f-\epsilon$) domain of the system. In particular, the transition through torus doubling to chaos via SNA, torus breaking to chaos via SNA and period doubling bifurcations of fractal torus are demonstrated with the aid of the two parameter ($f-\epsilon$) phase diagram. More interestingly, in order to approach the strange nonchaotic attractor, the existence of several new bifurcations on the torus corresponding to the novel phenomenon of torus bubbling are described. Particularly, we point out the new routes to chaos, namely, (1) two frequency quasiperiodicity $\to$ torus doubling $\to$ torus merging followed by the gradual fractalization of torus to chaos, (2) two frequency quasiperiodicity $\to$ torus doubling $\to$ wrinkling $\to$ SNA $\to$ chaos $\to$ SNA $\to$ wrinkling $\to$ inverse torus doubling $\to$ torus $\to$ torus bubbles followed by the onset of torus breaking to chaos via SNA or followed by the onset of torus doubling route to chaos via SNA. The existence of the strange nonchaotic attractor is confirmed by calculating several characterizing quantities such as Lyapunov exponents, winding numbers, power spectral measures and dimensions. The mechanism behind the various bifurcations are also briefly discussed.Comment: 12 pages, 12 figures, ReVTeX (to appear in Phys. Rev. E

Bifurcation and chaos in the double well Duffing-van der Pol oscillator: Numerical and analytical studies

The behaviour of a driven double well Duffing-van der Pol (DVP) oscillator for a specific parametric choice ($\mid \alpha \mid =\beta$) is studied. The existence of different attractors in the system parameters ($f-\omega$) domain is examined and a detailed account of various steady states for fixed damping is presented. Transition from quasiperiodic to periodic motion through chaotic oscillations is reported. The intervening chaotic regime is further shown to possess islands of phase-locked states and periodic windows (including period doubling regions), boundary crisis, all the three classes of intermittencies, and transient chaos. We also observe the existence of local-global bifurcation of intermittent catastrophe type and global bifurcation of blue-sky catastrophe type during transition from quasiperiodic to periodic solutions. Using a perturbative periodic solution, an investigation of the various forms of instablities allows one to predict Neimark instablity in the $(f-\omega)$ plane and eventually results in the approximate predictive criteria for the chaotic region.Comment: 15 pages (13 figures), RevTeX, please e-mail Lakshmanan for figures, to appear in Phys. Rev. E. (E-mail: [email protected]

Effect of Phase Shift in Shape Changing Collision of Solitons in Coupled Nonlinear Schroedinger Equations

Soliton interactions in systems modelled by coupled nonlinear Schroedinger (CNLS) equations and encountered in phenomena such as wave propagation in optical fibers and photorefractive media possess unusual features : shape changing intensity redistributions, amplitude dependent phase shifts and relative separation distances. We demonstrate these properties in the case of integrable 2-CNLS equations. As a simple example, we consider the stationary two-soliton solution which is equivalent to the so-called partially coherent soliton (PCS) solution discussed much in the recent literature.Comment: 11 pages, revtex4,Two eps figures. European Journal of Physics B (to appear

Secure Communication using Compound Signal from Generalized Synchronizable Chaotic Systems

By considering generalized synchronizable chaotic systems, the drive-auxiliary system variables are combined suitably using encryption key functions to obtain a compound chaotic signal. An appropriate feedback loop is constructed in the response-auxiliary system to achieve synchronization among the variables of the drive-auxiliary and response-auxiliary systems. We apply this approach to transmit analog and digital information signals in which the quality of the recovered signal is higher and the encoding is more secure.Comment: 7 pages (7 figures) RevTeX, Please e-mail Lakshmanan for figures, submitted to Phys. Lett. A (E-mail: [email protected]

On the simplest (2+1) dimensional integrable spin systems and their equivalent nonlinear Schr\"odinger equations

Using a moving space curve formalism, geometrical as well as gauge equivalence between a (2+1) dimensional spin equation (M-I equation) and the (2+1) dimensional nonlinear Schr\"odinger equation (NLSE) originally discovered by Calogero, discussed then by Zakharov and recently rederived by Strachan, have been estabilished. A compatible set of three linear equations are obtained and integrals of motion are discussed. Through stereographic projection, the M-I equation has been bilinearized and different types of solutions such as line and curved solitons, breaking solitons, induced dromions, and domain wall type solutions are presented. Breaking soliton solutions of (2+1) dimensional NLSE have also been reported. Generalizations of the above spin equation are discussed.Comment: 32 pages, no figures, accepted for publication in J. Math. Phy

Bifurcation and chaos in spin-valve pillars in a periodic applied magnetic field

We study the bifurcation and chaos scenario of the macro-magnetization vector in a homogeneous nanoscale-ferromagnetic thin film of the type used in spin-valve pillars. The underlying dynamics is described by a generalized Landau-Lifshitz-Gilbert (LLG) equation. The LLG equation has an especially appealing form under a complex stereographic projection, wherein the qualitative equivalence of an applied field and a spin-current induced torque is transparent. Recently chaotic behavior of such a spin vector has been identified by Zhang and Li using a spin polarized current passing through the pillar of constant polarization direction and periodically varying magnitude, owing to the spin-transfer torque effect. In this paper we show that the same dynamical behavior can be achieved using a periodically varying applied magnetic field, in the presence of a constant DC magnetic field and constant spin current, which is technically much more feasible, and demonstrate numerically the chaotic dynamics in the system for an infinitely thin film. Further, it is noted that in the presence of a nonzero crystal anisotropy field chaotic dynamics occurs at much lower magnitudes of the spin-current and DC applied field.Comment: 8 pages, 7 figures. To appear in Chao