Showing papers in "Physica D: Nonlinear Phenomena in 1986"

TL;DR: In this paper, the notion of qualitative information and the practicalities of extracting it from experimental data were considered, based on ideas from the generalized theory of information known as singular system analysis due to Bertero, Pike and co-workers.

TL;DR: A dynamical model for the immune system is described that is based on the network hypothesis of Jerne, and is simple enough to simulate on a computer, and has a strong similarity to an approach to learning and artificial intelligence introduced by Holland, called the classifier system.

TL;DR: It is suggested that since virtual automata have the computational capacity to fill many of the functional roles played by the primary biomolecules, there is a strong possibility that the ‘molecular logic’ of life can be embedded within cellular automata and that, therefore, artificial life is a distinct possibility within these highly parallel computer structures.

TL;DR: In this paper, it is argued that the border separating in space two possible solutions of the flow equations (as turbulent and laminar in pipe flows or boundary layers) moves with a constant mean velocity, depending on the control parameter.

TL;DR: In this article, it was shown that the parameters of a spiral wave can be modelled as s eigenvalues of a problem with unique solution, and the critical ingredients of the theory are the effects of curvature on the propagation of wavefronts in two-dimensional media, and dispersion of plane waves.

TL;DR: In this paper, the authors characterized the transition to chaos of the solutions to the Kuramoto-Sivashinsky equation through extensive numerical simulation, and showed that the attracting solution manifolds undergo a complex bifurcation sequence including multimodal fixed points, invariant tori, traveling wave trains, and homoclinic orbits.

TL;DR: This model is used to study the spontaneous emergence of autocatalytic sets from an initial set of simple building blocks, for example short strands of amino acids or nucleotides, and suggests that the critical diversity is not very large.

TL;DR: In this paper, a paradigm for describing dynamical systems that have both Hamiltonian and dissipative parts is presented, where features of generalized Hamiltonian systems and metric systems are combined to produce what are called metriplectic systems.

TL;DR: In this article, the authors examine systems of one and two nonlinear threshold elements, or neurons, of the kind used in electronic neural networks and find that the dynamics can be complex, in contrast to the simpler behavior displayed when they are of the standard resistor-capacitor variety.

TL;DR: In this paper, the co-moving mutual information flow is introduced, which shows the selective transmission of the information at some speed, and the spatial structures of the vectors are investigated.

TL;DR: In this article, it was shown that using multi-scale expansions conventionally employed in the theory of nonlinear waves one can transform systems integrable by the IST method into other systems of this type.

TL;DR: In this paper, the authors studied the steady solutions of the Kuramoto-Sivashinsky equation and showed that for small c 2 there is a periodic solution and an infinite set of quasi-periodic solutions as asserted by Moser's twist map theorem.

TL;DR: In this article, a large number of new geometric, ergodic and statistical properties of the Kuramoto-Sivashinsky equation were presented for modeling interfacial turbulence in various physical contexts.

TL;DR: In this paper, a model retaining a discrete set of cantor approaching a boundary circle gives the Markov chain description of Hanson, Cary and Meiss, and the inclusion of cantori surrounding island chains, and islands about islands, etc.

TL;DR: It is argued that a unification of the theories of pattern formation and associative memory is required to account for the formation and alteration of spatial patterns in neural activity observed experimentally during classical Pavlovian conditioning.

TL;DR: It is shown that as a class the FA's are equivalent to CA's, in the sense that the same array of space-generation values can be produced; they must be generated in a different order, however.

TL;DR: In this article, a Poisson bracket is determined using the method of Arnold, namely reduction from canonical variables in the Lagrangian (material) description, and the Hamiltonian form for the equations of a liquid drop with a free boundary having surface tension is demonstrated.

TL;DR: The inverse problem for the two-dimensional Schrodinger operator on the data from one energy level is solved in a special class of "finite zone" or "algebraic" operators as discussed by the authors.

TL;DR: In this article, the time-dependent generalized Ginzburgland-landau equation is studied in the presence of low-level external noise and it is found that themicroscopic noise plays an important role in themacroscopic dynamics of the system, in which the random nature of the external noise plays a crucial role.

TL;DR: Two major types of foraging organisation in ants are described and compared, being illustrated with experimental data and mathematical models, and the first is discussed in relation to spatial specialisation, foraging density, individual learning and genetic programming.

TL;DR: In this article, an abstract diffusion-convection equation is introduced and the physical content of this equation is compatibility with equilibrium thermodynamics, which means that properties of solutions of the abstract diffusion convection equation are mathematical formulations of the experience on which thermodynamics is based.

TL;DR: In this paper, a detailed study of a mapping on a two-dimensional manifold is made, in which the mapping describes a system subject to periodic forcing, in particular an imperfectly elastic ball bouncing on a vibrating platform.

TL;DR: It is demonstrated that the Boltzmann learning algorithm is capable of finding sets of weights which turn hidden units into useful higher-order feature detectors capable of solving symmetry problems.

TL;DR: In this article, a general theory which is valid near onset and which can account for each of these features was developed and a universal equation of Ginzburg-Landau type with complex coefficients was investigated numerically and analytically in one and two spatial dimensions.

TL;DR: In this article, a summary of the significance of the star-triangle or Yang-Baxter equations in the solution of two-dimensional statistical mechanical models is given and the extension to the three-dimensional tetrahedron relations is quoted and it is shown how this can be used to obtain the partition function of the Zamolodchikov model for an n × ∞ − ∞ lattice.

TL;DR: In this article, the authors revisited the solitary wave collisions studied by Ablowitz, Kruskal, and Ladik and showed that the resonance that they observed in collisions in the Φ4 nonlinear Klein-Gordon equation is one of a sequence of resonances that occur in that theory.