Showing papers in "Physica D: Nonlinear Phenomena in 1994"

TL;DR: An overview of an inductive framework-hierarchical ϵ-machine reconstruction—in which the emergence of complexity is associated with the innovation of new computational model classes is presented, along with an analysis of the constraints on the dynamics of innovation.

TL;DR: In this article, sufficient conditions are derived for the delay independent stability of Hopfield's graded response networks of the type dxi(t)/dt = -bixi(t) + Σnj = 1aijfj(μjxj(t - τij)) +Fi(t), i = 1, 2, …, n) when the external inputs Fi are held temporally uniform.

TL;DR: In this paper, a methodology introduced by Fuchssteiner and the author is used to derive a class of physically important integrable evolution equations, which are integrably generalizations of the Korteweg-deVries (KdV), of the modified KdV, of the nonlinear Schrodinger (NLS), and of the sine-Gordon equations.

TL;DR: In this paper, it was shown that series arrays of N identical overdamped Josephson junctions have extremely degenerate dynamics and that such arrays have N − 3 constants of motion for all N ⩾ 3.

TL;DR: In this paper, the authors describe a model of a stock market in which independent adaptive agents can buy and sell stock on a central market and the overall market behavior is an emergent property of the agents' behavior.

TL;DR: In this paper, a renormalization method has been proposed to determine (α, β) from the first principles (i.e., from the Hamiltonian) of the Fokker-Planck-Kolmogorov equation.

TL;DR: In this article, the authors developed a new, computationally efficient approach to choosing τ that quantifies reconstruction expansion from the identity line of the embedding space, and showed that reconstruction expansion is related to the concept of reconstruction signal strength and that increased expansion corresponds to diminished effects of measurement error.

TL;DR: In this article, it was shown that a solution of incompressible Euler equations with Holder continuous velocity of order h > 1 3 conserves kinetic energy, but not necessarily if h ≤ 1 3.

TL;DR: The extent to which symmetry breaking and other impediments are general phenomena in any GA search is discussed, and four “epochs of innovation” in which new CA strategies for solving the problem are discovered by the GA are identified.

TL;DR: In this article, a lattice model of coevolution of strategies for two-person 2 × 2 matrix games is introduced, which allows evolution in an unbounded space of strategies.

TL;DR: In this article, a catalogue of symmetry reductions for the nonlinear heat equation is given, including new reductions for linear heat equation and exact solutions of exact solutions for cubic heat equation for cubic f (u) in terms of the roots of f(u) = 0.

TL;DR: In this paper, a thermodynamically consistent continuum theory for solid-solid phase transitions is developed, in which deformation dominates heat and mass transfer, and the growth of one phase at the expense of another is modeled by configurational forces.

TL;DR: In this paper, it was shown that the nonlinear partial differential equation, ( u t + u x ) xx = 1/2( u x 2 ) x, is a completely integrable, bi-variational, and bi-Hamiltonian system.

TL;DR: In this article, a model of a large population of identical excitable neurons with a global slowly decaying inhibitory coupling is studied and its patterns of synchrony are examined and a method for calculating the stability of cluster states is described and used for investigating the dynamical behavior of the network versus the parameters that describe neurons and synapses.

TL;DR: In this paper, the authors review experimental evidence for earthquake scale-invariance and propose a model of random defect interaction which, without additional assumptions, seems to explain most of the available empirical results.

TL;DR: Relevance of the clustering to ecological, immune, neural, and cellular networks is discussed, with the emphasis on partially ordered states with chaotic itinerancy, and an extension allowing for the growth of the number of elements is given in connection with cell differentiation.

TL;DR: By focussing attention on close returns of a trajectory to itself, the existence of deterministic dynamics underlying a time series can be detected even in very short data sets, providing a practical means of detecting determinism in moderate-dimensional noisy systems, or low-dimensional systems with large Lyapunov exponents such as computer random number generators.

TL;DR: In this article, a simple kinematical model for spiral waves in weakly excitable media is proposed, where the model is formulated in terms of the motion of curves with free ends.

TL;DR: The generalized complex Ginzburg-Landau equation (GGLE) is a model for fluid turbulence described by the incompressible Navier-Stokes equations as mentioned in this paper, which is a dissipative version of the Hamiltonian nonlinear Schrodinger equation possessing solutions that form localized singularities.

TL;DR: In this paper, a periodically closed sequence of Backlund transformations (BT) and the Painleve equations P2-P6 are derived from the discrete symmetries of these systems.

TL;DR: In this article, a mechanism for the development of strange non-chaotic attractors from two-frequency quasiperiodic attractors in a logistic map is described.

TL;DR: In this paper, the authors consider the dynamics near the transition to chaotic attractors and obtain the characteristic behaviors near this transition using a simple analyzable model, consistent with the conjecture that these results are universal for the class of systems considered.

TL;DR: In this article, an overview of the current status of inverse methods and data assimilation for nonlinear ocean models is given, and the most promising solution methods like simulated annealing, the representer method, and sequential methods based on Monte Carlo simulations are discussed with special focus on applications with nonlinear dynamics.

TL;DR: In this paper, long-term particle tracking is used to study chaotic transport experimentally in laminar, chaotic, and turbulent flows in an annular tank that rotates sufficiently rapidly to insure two-dimensionalality of the flow.

TL;DR: It is concluded that a mixture of many length scales (including some relatively long ones) in DNA sequences is responsible for the observed 1 f -like spectral component.

TL;DR: In this paper, the authors reviewed the evidence for irregular climatic change between warm (thermos) and cold (cryos) extremes, concentrating on the last two million years, the Quaternary.

TL;DR: In this paper, exact solitary wave solutions of the one-dimensional quintic complex Ginzburg-Landau equations are obtained using a method derived from the Painleve test for integrability.

TL;DR: In this article, a principle of locomotor control in an unpredictably changing environment is presented on the basis of neurophysiology and biomechanics from the perspective of nonlinear dynamics theory, which emerges as a limit cycle generated through global entrainment among the neuro-musculo-skeletal system and the environment.

TL;DR: In this paper, the authors studied the dynamics of vortices in time-dependent Ginzburg-Landau theories in the asymptotic limit when the vortex core size is much smaller than the inter-vortex distance.

TL;DR: In this article, the stabilization of period doubling bifurcations for discrete-time nonlinear systems is investigated, and it is shown that generically such bifurbcations can be stabilized using smooth feedback, even if the linearized system is uncontrollable at criticality.