The origin and evolution of a strange attractor in the system of coupled oscillators

422

Nonlinear

science

abstracts

avowedly pehnomenological or putatively rigorous, all rely on a hydrodynamic mechanism. The theoretical treatments of mathematicians, based on the differential topology of '*dynamical systems", appear not to be in agreement with long time tails. Recent experiments with polystyrene spheres, observed by light scattering, claim to see the effect of long tilne tails. These experiments may be interpreted as observations of the Stokes-Boussinesq effect expected for "macroscopic" spheres, but not justified for truly microscopic, molecular sized, particles. While long time tails may yet be rigorously established by computer simulation, theory, and experiment, it is argued in this paper that this has not happened yet. Moreover, a firm basis for serious doubt is raised. JOURNAL: none given 391

(B5,13) THE ORIGIN AND EVOLUTION OF A STRANGE ATTRACTOR IN THE SYSTEM OF COUPLED OSCILLATORS, V. I. Sbftnev, Academy of Sciences of the USSR, Leningrad Nuclear Physics Institute, Leningrad, USSR. Two pairs of coupled nonlinear differential equations describe the activity of two interacting neuron populations. Each population consists of two kinds of neurons, excitatory and inhibitory ones. Stochastic oscillations in the system at the moment of sta.bility breakdown of the 3-periodic orbit originate in accordance with Pomeau-Manneville Scenario. The evolution of stochastic oscillations is investigated by graphic constructions of the induced diffeomorphisms. JOURNAL: none given 392

(M1,14) A SIMPLE DERIVATION OF THE STOCHASTIC EIGENVALUE EQUATION IN THE TRANSITION FROM QUASIPERIODICITY TO CHAOS, Bambi Hu, Department of Physics, University of Houston, Houston, TX 77004, USA. equation, A simple derivation of the stochastic eigenvalue previously obtained by irrational decimation of functional integrals, is given to show the universal scaling behavior of external noise in the transition from quasiperiodicity to chaos in dissipative systems. JOURNAL: none given 393

(M4,15) A TWO-DIMENSIONAL SCALING THEORY OF INTERMITTENCY, B. Hu, Department of Physics, Univeristy of Houston, Houston, TX 77004, USA. A two-dimensional scaling theory of intermittency in the presence of general area-preserving maps of noise is modeled on tangent bifurcation The two-dimensional functional incorporating different universality classes. equations eigenvalue associated and the renormalization equations, group The complete describing deterministic and stochastic perturbations are derived. behavior of the length of are found, and the scaling eigenvalue spectra laminarity is discussed. JOURNAL: Physics Letters, Volume 91A, Number 8, October, 1982 EXACT SOLUTIONS TO THE RENORMALIZATION-GROUP FIXED-POINT EQUATIONS (M4,15) FOR INTERMITTENCY IN TWO-DIMENSIONAL MAPS, B. Hu, University of Houston, Houston, TX 77004, USA, J. Rudnick, Department of Physics, University of California, Davis, CA 95616, USA. Using a differential-equation formulation, we have found the exact solutions to the fixed-point functions of the renormalization-group equations for intermittency based on a class of two-dimensional area-preserving maps. JOURNAL: Physical Review A, Volume 26, Number 5, November, 1982

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