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Showing papers in "Physica D: Nonlinear Phenomena in 1987"


Journal ArticleDOI
TL;DR: In this article, the authors derive a new global characterization of the normal forms of amplitude equations describing the dynamics of competing order parameters in degenerate bifurcation problems, using an appropriate scalar product in the space of homogeneous vector polynomials, and show that the resonant terms commute with the group generated by the original critical linear operator.

433 citations


Journal ArticleDOI
TL;DR: In this article, the Lyapunov analysis is used to study the high-dimensional chaotic states of a class of delay-differential equations with time delayed feedback such as nonlinear optical resonators.

355 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived a set of differential equations for the eigenvalues and eigenvectors of the stability matrix of a dynamical system, as well as for the Lyapunov exponents and the corresponding eigenvector.

276 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined systems of one and two nonlinear threshold switching elements (neurons) of the kind used in electronic neural networks and found that the collective behavior of a network of multiple neurons can be underdamped even when the individual connections are overdamped.

224 citations


Journal ArticleDOI
TL;DR: In this article, a non-integrability criterion on the basis of Ziglin's theorem for two degrees of freedom Hamiltonians with a homogeneous potential of integer degree was given.

188 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that three-dimensional incompressible flows lacking parity-invariance (reversal of coordinates) can display large-scale instability analogous to the α-effect of magnetohydrodynamics, but essentially anisotropic.

180 citations


Journal ArticleDOI
TL;DR: In this paper, a large class of systems of N -equations which possess (N + 1) purely differential, compatible Hamiltonian structures are presented, which are thus tri-Hamiltonian.

179 citations


Journal ArticleDOI
TL;DR: In this paper, a time series analysis of observed solar radio pulsations suggests that there must be a low-dimensional attractor and that the power spectrum cannot be interpreted as a superposition of periodic components.

169 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigate boundary metamorphoses characterized by a sudden replacement of the basin boundary's accessible orbit by a saddle periodic orbit, and show that typically only one of them can be reached or accessed directly from a given basin.

160 citations


Journal ArticleDOI
TL;DR: In this article, the authors define an entropy function S(a) which measures large deviations of the Liapunov characteristic exponents of certain hyperbolic dynamical systems.

150 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the areas of the resonances, as well as the turnstile areas, can be obtained from the actions of homoclinic orbits.

Journal ArticleDOI
TL;DR: In this paper, solitary-wave solutions of model equations for long waves that feature a general form of linear dispersion are derived and sufficient conditions for the non-linear stability of such solutions are derived.

Journal ArticleDOI
TL;DR: The local structure theory as mentioned in this paper is a sequence of finitely-parameterized models of the statistical features of a cellular automaton's evolution, which is a powerful method for characterization and classification of cellular automata.

Journal ArticleDOI
TL;DR: In this article, the Geometric Model of Crystal Growth (GMMG) is used to analyze the dynamics of Dendritic Growth. But the model is not suitable for the case of solitons.

Journal ArticleDOI
TL;DR: In this article, the Painleve test for partial differential equations is examined in detail and shown to provide a unified approach to the integrable properties of both ordinary and PDEs.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the long-time behavior of solutions to the Ginzburg-Landau partial differential equation and showed that a finite-dimensional attractor captures all the solutions.

Journal ArticleDOI
TL;DR: In this article, the Schrodinger equations with attraction and repulsion (NSE(+) and NSE(−)) and the Korteweg-de Vries equation perturbed by small dissipative terms are considered.

Journal ArticleDOI
TL;DR: In this paper, the excitation of multi-level systems by a periodic field is considered in the regime of quasiclassical diffusion which takes place in the region of classical dynamical chaos.

Journal ArticleDOI
TL;DR: In this paper, the dynamics of the periodic orbits of the generalized Arnold-Sinai cat maps were transformed into modular arithmetic in suitable domains of quadratic integers, and all periodic orbits were classified.

Journal ArticleDOI
TL;DR: In this paper, the combined dynamical effects of elasticity and a rotating reference frame are explored for structures in a zero gravity environment, and this approach is applied to analyze in detail the dynamics of a specific prototypical structure.

Journal ArticleDOI
TL;DR: In this article, the authors studied a model open-flow system: the time-dependent generalized Ginzburg-Landau equation under conditions when it is convectively (i.e. spatially) unstable.

Journal ArticleDOI
TL;DR: In this article, the authors studied a two-parameter family of differential equations in R 4 that governs the dynamics of two coupled planar oscillators, where each oscillator has a unique periodic solution that is attracting and the uncoupled product system has an invariant torus that is attracted.

Journal ArticleDOI
TL;DR: In this paper, the authors extract information from a time displacement matrix through its singular values, and the associated orthogonal matrices, and show that asymptotic, after a long time, they depend only on the location in phase space, and not on the orbit.

Journal ArticleDOI
TL;DR: In this article, a spiral-shaped wave of chemical activity propagating in a 1 mm layer of an excitable solution of the Belousov-Zhabotinskii reaction is analyzed quantitatively for a 5 min time interval in a 4.5 × 4 mm area.

Journal ArticleDOI
TL;DR: In this article, the effects of roundoff errors on discrete-time dynamical systems were investigated and it was shown that computer-generated orbits terminate in loops whose lengths scale with the machine precision in a universal way.

Journal ArticleDOI
TL;DR: In this paper, the existence and properties of strange non-chaotic attractors of quasiperiodically forced nonlinear dynamical systems are discussed, and it is shown that these attractors are typical in the sense that they exist on a set of positive Lebesgue measure in parameter space.

Journal ArticleDOI
TL;DR: In this paper, a highly nonlinear hydrodynamic equation proposed by Johnson is solved exactly, by gauge transforming (GT) it to the mixed nonlinear Schrodinger equation, and generalized further, to generate a hierarchy of integrable higher-order nonlinear systems including some known equations, along with their Lax pairs, infinite sets of conserved quantities and exact solutions.

Journal ArticleDOI
TL;DR: In this article, generic bifurcations of equilibria in one-parameter Hamiltonian systems with symmetry group Γ on the generalized eigenvalues of the linearized system go through zero.

Journal ArticleDOI
TL;DR: In this paper, a modified Fitz Hugh-Nagumo model was used to study numerically the scroll rings in a three-dimensional active medium, which consists in gradual extension and drifting of the scroll ring filament.

Journal ArticleDOI
TL;DR: In this article, the L multi-soliton solution corresponding to poles of order L of the function r(k), and their asymptotic behaviors are obtained. But the weakly bound states of the two-and three-solomon solutions are explicitly given (i.e. double and triple pole solutions).