The recently developed [12, 14, 24, 15] quantum surface of section method is applied to a search for extremely high-lying energy levels in a simple but generic Hamiltonian system between integrability and chaos, namely the semiseparable 2dim oscillator. Using the stretch of 13,445 consecutive levels with the sequential number around 1.8 ·107 (eighteen million) we have clearly demonstrated the v...

We study the bifurcation diagram of the Rössler system. It displays the various dynamical regimes of the system (stable or chaotic) when a parameter is varied. We choose a diagram that exhibits coexisting attractors and banded chaos. We use the topological characterization method to study these attractors. Then, we detail how the templates of these attractors are subtemplates of a unique templa...

Diffusionless Lorenz equations (DLE) are a simple one-parameter version of the wellknown Lorenz model, which was obtained in the limit of high Rayleigh and Prandtl numbers, physically corresponding to diffusionless convection. A simple control method is presented to control chaos by using periodic parameter perturbation in DLE. By using the generalized Melnikov method, the parameter conditions ...

After a brief introduction to a new chaotic stream cipher Mmohocc which utilizes the fundamental chaos characteristics of mixing, unpredictability, and sensitivity to initial conditions, we conducted the randomness statistical tests against the keystreams generated by the cipher. Two batteries of most stringent randomness tests, namely the NIST Suite and the Diehard Suite, were performed. The r...

We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction k...

Different discrete models of population dynamics of certain insects have been investigated under various feasible conditions within the framework of nonlinear dynamics. Evolutionary phenomena are discussed through bifurcation analysis leading to chaos. Some tools of nonlinear dynamics, such as Lyapunov characteristic exponents (LCE), Lyapunov numbers, correlation dimension, etc. are calculated ...

For the first time we present the consideration of the antiferromagnetic Ising model in case of fully developed chaos and obtain the exact connection between this model and chaotic repellers. We describe the chaotic properties of this statistical mechanical system via the invariants characterizing a fractal set and show that in chaotic region it displays phase transition at positive ”temperatur...

We present a theory where the statistical mechanics for dilute ideal gases can be derived from random matrix approach. We show the connection of this approach with Srednicki approach which connects Berry conjecture with statistical mechanics. We further establish a link between Berry conjecture and random matrix theory, thus providing a unified edifice for quantum chaos, random matrix theory an...

We present experimental results for pattern formation in Rayleigh-Bénard convection of a fluid with a Prandtl number σ ≃ 4. We find that the spiraldefect-chaos (SDC) attractor which exists for σ ≃ 1 has become unstable. Gradually increasing the temperature difference ∆T from below to well above its critical value ∆Tc no longer leads to SDC. A sudden jump of ∆T from below to above ∆Tc causes con...

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