This paper examines the most probable route to chaos in high-dimensional dynamical systems function space (time-delay neural networks) endowed with a probability measure in a computational setting . The most probable route to chaos (relative to the measure we impose on the function space) as the dimension is increased is observed to be a sequence of Neimark-Sacker bifurcations into chaos. The a...

The presence of chaos and quantum chaos is shown in two different nuclear systems. We analyze the chaotic behaviour of the classical SU(2) Yang–Mills– Higgs system, and then we study quantum chaos in the nuclear shell model calculating the spectral statistics of A = 46–50 atomic nuclei.

We present the first report on chaos synchronization between two unidirectionally linearly and non-linearly coupled systems with multiple time-delays and using the Razumikhin-Lyapunov approach find the existence and stability conditions for different synchronization regimes. The approach is tested on the famous nonlinear models-Ikeda, Mackey-Glass and Lang-Kobayashi systems.There is continued g...

We address the problem of quantum chaos: Is there a rigorous, physically meaningful definition of chaos in quantum physics? Can the tools of classical chaos theory, like Lyapunov exponents, Poincaré sections etc. be carried over to quantum systems? Can quantitative predictions be made? We show that the recently proposed quantum action is well suited to answer those questions. As an example we s...

– We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and...

We argue that transient chaos in deterministic dynamical systems is a major source of noiseinduced chaos. The line of arguments is based on the fractal properties of the dynamical invariant sets responsible for transient chaos, which were not taken into account in previous works. We point out that noise-induced chaos is a weak noise phenomenon since intermediate noise strengths destroy fractali...

It is well known that most conventional control methods and many special techniques can be used for chaos control [Chen & Dong, 1998] whether the purpose is to reduce “bad” chaos or to introduce “good” chaos. Numerous control methodologies have been proposed, developed, tested and applied. Due to its great potential in nontraditional applications such as those found within the context of physic...

One of the remarkable achievements in science in the 20th century is the discovery of dynamical chaos. Using this paradigm, many problems in modern science and engineering can be realistically simulated and analyzed via the tools of nonlinear dynamics. The quest for understanding and explaining chaos in real physical systems has led to the creation of new mathematical techniques. Indeed, there ...

Most current hyper-CASE systems place emphasis on how hypermedia functionality can be used in implementing CASE systems, with the hypermedia as a means of supporting the management of software life cycle documents in a non-integrated CASE environment. In this paper, we argue that hypermedia should be integrated with CASE in a seamless manner and must be able to support integrated CASE systems. ...