The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddlenode bifurcation, boundary crisis, and interior crisis. The...

We demonstrate that the pedestal components observed in the power spectra of a directly modulated laser diode, which were interpreted as a sign of instability of the periodic regime, are an indication of the coexistence of a chaotic regime with the periodic one. We present the underlying dynamics behind the rise of these pedestals, showing two different situations in which the pedestals appear....

L et us apply our newly acquired tools to the fundamental diagnostics in dynamics: Is a given system ‘chaotic’? And if so, how chaotic? If all points in example 2.3 a neighborhood of a trajectory converge toward the same orbit, the attractor is a fixed point or a limit cycle. However, if the attractor is strange, any two section 1.3.1 trajectories x(t) = f (x0) and x(t)+δx(t) = f (x0 + δx0) tha...

We have uncovered a phenomenon in coupled chaotic oscillators where a subset of Lyapunov exponents, which are originally zero in the absence of coupling, can become positive as the coupling is increased. This occurs for chaotic attractors having multiple scrolls, such as the Lorenz attractor. We argue that the phenomenon is due to the disturbance to the relative frequencies with which a traject...

A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from those of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace the usual fixed-point population solutions. We observe the familiar period-doubling and chaotic-band-splitting attractor cascades of unimodal maps but in s...

A chaotic model of spontaneous (without external stimulus) neuron firing has been analyzed by mapping the irregular spiking time-series into telegraph signals. In this model the fundamental frequency of chaotic Rössler attractor provides (with a period doubling) the strong periodic component of the generated irregular signal. The exponentially decaying broad-band part of the spectrum of the Rös...

A novel generation method of chaotic attractor is introduced in this paper. The underlying mechanism involves a simple three-dimensional time-varying system with simple time functions as control inputs. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable system parameters. The largest Lyapunov exponent of the system has bee...

In this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with ...

A chaotic attractor solution of the Lorenz system [1] with foliated structure is topologically characterized. Its template permits to both summarize the organization of its periodic orbits and detail the topology of the solution as a branched manifold. A template of an attractor solution of the Chen system [2] with a similar foliated structure is also established.

An electronic circuit realization of a modified Lorenz system, which is multiplier-free, is described. The well-known butterfly chaotic attractor is experimentally observed verifying that the proposed modified system does capture the essential dynamics of the original Lorenz system. Furthermore, we clarify that the butterfly attractor is a compound structure obtained by merging together two sim...