混沌动力学

The ability of nonlinear dynamical systems to process incoming information is a key problem of many fundamental and applied sciences. Information processing by computation with attractors (steady states, limit cycles and strange attractors)…

The dynamical bifurcations of a laser with a saturable absorber were calculated, with the 3-2 level model, as function of the gain parameter. The average power of the laser is shown to have specific behavior at bifurcations. The succession…

We study the instantaneous and local energy injection in a turbulent shear flow driven by volume forces. The energy injection can be both positive and negative. Extremal events are related to coherent streaks. The probability distribution…

Gear box dynamics is characterised by a periodically changing stiffness and a backlash which can lead to a loss of the contact between the teeth. Due to backlash, the gear system has piecewise linear stiffness characteristics and, in…

We report our results on non-periodic experimental time series of pressure in a spark ignition engine. The experiments were performed for a low rotational velocity of a crankshaft and a relatively large spark advance angle. We show that the…

Hierarchy of one and many-parameter families of random trigonometric chaotic maps and one-parameter random elliptic chaotic maps of $\bf{cn}$ type with an invariant measure have been introduced. Using the invariant measure…

We analyse the combustion process in a spark ignition engine using the experimental data of an internal pressure during the combustion process and show that the system can be driven to chaotic behaviour. Our conclusion is based on the…

We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…

Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions…

We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1-$d$ map models whose slope is everywhere 1 (therefore the Lyapunov exponent is zero) but with random quenched discontinuities and quasi-periodic…

We give a hierarchy of many-parameter families of maps of the interval [0,1] with an invariant measure and using the measure, we calculate Kolmogorov--Sinai entropy of these maps analytically. In contrary to the usual one-dimensional maps…

Chaotic dynamics of the dripping faucet was investigated both experimentally and theoretically. We measured continuous change in drop position and velocity using a high-speed camera. Continuous trajectories of a low-dimensional chaotic…

We introduce a dissipative version of the Zhang's model of Self-Organized Criticality, where a parameter allows to tune the local energy dissipation. We analyze the main dynamical features of the model and relate in particular the Lyapunov…

We describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic. (This is an alternative to the usual approach of computing the largest Lyapunov exponent.) Our method is a 0-1 test for chaos…

We consider a simple model of particle transport on the line defined by a dynamical map F satisfying F(x+1) = 1 + F(x) for all x in R and F(x) = ax + b for |x| < 0.5. Its two parameters a (`slope') and b (`bias') are respectively symmetric…

We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this…

The time evolution equations of a simplified isolated ideal gas, the "tetrahe- dral" gas, are derived. The dynamical behavior of the LMC complexity [R. Lopez-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A 209, 321 (1995)] is studied in…

We study the algebraic decay of the survival probability in open hierarchical graphs. We present a model of a persistent random walk on a hierarchical graph and study the spectral properties of the Frobenius-Perron operator. Using a…

Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter \lambda of the system is modified. Complex patterns on the plane are visualised as a consequence of basins'…

We report experimental control of chaos in an electronic circuit at 43.9 MHz, which is the fastest chaos control reported in the literature to date. Limiter control is used to stabilize a periodic orbit in a tuned collector transistor…