Showing papers in "Physica D: Nonlinear Phenomena in 1982"

TL;DR: In this paper, the chaotic attractors of a delay differential equation were studied and the dimension of several attractors computed directly from the definition agreed to experimental resolution with the dimension computed from the spectrum of Lyapunov exponents according to a conjecture of Kaplan and Yorke.

TL;DR: In this paper, a new approach to soliton equations, based on τ functions (or Hirota's dependent variables), vertex operators and the Clifford algebra of free fermions, is applied to study a new hierarchy of Kadomtsev-Petviashvili type equations (the BKP hierarchy).

TL;DR: In this paper, a method for finding intersections of a numerically integrated trajectory with a surface of section is described, where the intersections are defined as the intersections of the intersection of the trajectory and the surface of the section.

TL;DR: In this article, the complex Lorenz equations were studied in a frame rotating with the limit cycle frequency and the complex parameters r and a were defined by r = r1 + ir2; a = 1 − ie and σ and b are real.

TL;DR: In this article, an approach to collective aspects of the neocortical system is formulated by methods of modern nonlinear nonequilibrium statistical mechanics, which are first spatially averaged over columnar domains.

TL;DR: In this paper, the dynamical behavior of a large one-dimensional system obeying the cubic complex Ginzburg-Landau equation is studied numerically as a function of parameters near a supercritical bifurcation.

TL;DR: The Lorenz equations are derived systematically from amplitude equations of weakly nonlinear dispersively unstable physical systems near criticality when weak dissipation is added as discussed by the authors, and they are only valid if the undamped neutral curve is not destabilised by the addition of weak dispersive effects.

TL;DR: In this paper, the authors studied the scaling behavior of a return map of a circle onto itself on a torus and found that the map T(θ)=θ+Ω−( K 2π ) sin 2πθ exhibit unusual scaling behavior for K = 1.

TL;DR: In this paper, the authors present global phenomena of pattern formation in stationary reaction-diffusion equations, possessing Turing's diffusion-induced instability, which appear typically in mathematical biology, by integrating two complementary approaches-analytical and numerical.

TL;DR: In this paper, a discrete one-dimensional system with the 2-3 power onsite potential was studied, and the authors derived an approximate oscillating solution with a quasi-infinite lifetime.

TL;DR: In this article, the spectral transform ∂u / ∂x = { A ( ζ )+ B ( x, ζ)} · u, where u is an n-element column vector and A (ζ) and B (x, ζ), are n x n matrices, is considered.

TL;DR: In this article, the energy levels of a charged particle with an anisotropic mass tensor are calculated on the basis of classically ergodic trajectories, and the trace of the semiclassical Green's function is a sum over all periodic orbits, and can be evaluated by a transformation which Kac used in the discussion of an Ising lattice with long range interaction.

TL;DR: In this paper, the construction of the reduced space and the reduced Hamiltonian for the semisimple 1:1 resonance case was described, and the results were related to problems in physics on "degeneracies" due to symmetries of classical two-dimensional harmonic oscillators and their quantum analogues for the hydrogen atom.

TL;DR: In this paper, the authors considered the surface-tension-driven convection in a liquid film and showed that if the film is nearly thermally insulated, the longitudinal dimension of the convective cells is significantly greater than the film thickness.

TL;DR: In this paper, the structure of a reaction cell with diffusion coupling was analyzed and the structure was shown to agree with results reported for a variety of dynamic systems, such as aperiodic (chaotic) states.

TL;DR: The existence of chaotic orbits for area preserving diffeomorphisms of the plane is proved in this article for polynomials of degree two, derived from the discretized logistic equation.

TL;DR: In this paper, the derivation of superposition rules, which express the general solution of ordinary differential equations, is studied in terms of a finite number of particular solutions, where the point of departure is Lie's criterion according to which such a rule exists if and only if the vector fields η (x, t ). ∇ generate a finite dimensional Lie algebra.

TL;DR: In this article, the effect of a small amount of noise on the standard mapping is considered and the diffusion coefficient contains a term proportional to the reciprocal of the variance of the noise term.

TL;DR: In this paper, the dynamics of systems of vortices are considered and it is shown that in the phase space of the system of any finite number of VMs there exists a set of initial conditions of positive measure for which the motion of the VMs is quasi-periodical.

TL;DR: It is found that irregularity sets in when two homoclinic structures are present and, in this case, many and continual homocinic crossings occur throughout the irregular time series.

TL;DR: The upper bound on the minimum number of modes for a qualitatively correct Galerkin approximation to the two-dimensional Benard convection is discussed in this paper, where selection rules are introduced to ensure that the approximation satisfies the same energy balance conditions as the exact solution.

TL;DR: In this paper, a simple stochastic model of a particle diffusing randomly in an external two-well potential is proposed to stimulate the onset of turbulence in a medium aspect ratio cylindrical Rayleigh-Benard cell.

TL;DR: In this article, a modified Karhunen-Loeve transform is derived using a weighted Sobolev norm, which optimizes the approximation of the higher derivative terms in numerical simulations of partial differential equation and reduces the sizes of the associated system of ordinary differential equations.

TL;DR: In this paper, the boundary between regular ordered motion on invariant curves and irregular chaotic motion is given by the radius of convergence of the Taylor series, where successive terms of the series oscillate wildly, due to the presence of small divisors.

TL;DR: In this article, a simple focusing-dispersing billiard system whose phase space simultaneously exhibits the full range of possible Hamiltonian syste, orbit behavior over a continuous range of system parameter values is presented.

TL;DR: The canonical structure of nonlinear evolution equations in 1 + 1 dimensions solvable in terms of an N × N inverse scattering problem is discussed in this paper, and a direct proof of the involutive character of the infinite number of conserved quantities is given for the general case as well as the reduced case.

TL;DR: In this paper, the authors consider one-dimensional propagation both of body and surface waves and show that if a wave packet propagates without altering its shape it must, of necessity, be a solution of a linear wave equation and in this sense, (body) solitary waves do not exist.

TL;DR: In this paper, a new diagrammatic representation for Hamiltonian systems with three phase space dimensions is presented, which allows an easy way to find KAM boundaries and island in the Poincare mapping and lead thereby to a complete description of the geography of the mapping.