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Showing 1 to 9 of 9 for “"complex Ginzburg-Landau equation"”.
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A General Study of the Complex Ginzburg-Landau Equation
… I study a nonlinear partial differential equation, the complex Ginzburg-Landau (CGL) equation. I first employed the perturbative field-theoretic renormalization group method to investigate the critical dynamics near the continuous non-equilibrium transition limit in this equation with …
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The nonlinear Schroedinger limit of the complex Ginzburg-Landau equation.
This work consists of a study of the complex Ginzburg-Landau equation (CGL) as a perturbation of the nonlinear Schrodinger equation (NLS) in one dimension under periodic boundary conditions. Using an averaging technique which is similar to a Melnikov method for pde's, necessary conditions are …
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A study of the effects of spatially localized time-delayed feedback schemes on spatio-temporal patterns
… perturbations within chaotic states of the cubic complex Ginzburg-Landau equation We present an investigation of two model systems: the Gray-Scott reaction-diffusion equation and the complex Ginzburg-Landau equation. Specifically we numerically study two models characterized by exhibiting various …
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Localised solutions of the parametrically driven Ginzburg-Landau and nonlinear Schrӧdinger equations
… localised solutions of the parametrically driven Ginzburg-Landau equation and its nonlinear Schrӧdinger limit. We begin with a detailed analysis of the Faraday Resonance experiment, in which the driven complex Ginzburg-Landau equation (CGLE) arises, and an examination of how the CGLE appears as …
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Stochastic effects on extinction and pattern formation in the three-species cyclic May–Leonard model
… a coarse-grained Langevin description, i.e. the Complex Ginzburg Landau equation with stochastic noise in one complex field. We see that when one restricts the internal reaction noise to small amplitudes, one can obtain a simple form for the stochastic noise correlations that modify the Complex …
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Dynamical systems approach to one-dimensional spatiotemporal chaos -- A cyclist's view
… waves) near the first instability of the complex Ginzburg-Landau equation, and check their role in pattern formation. Third, we present the extensive numerical exploration of the Kuramoto-Sivashinsky system in the chaotic regime: structure of the equilibrium solutions, our search for the …
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Control, Dynamics, and Epidemic Spreading in Complex Systems
… problems involving the control and dynamics of complex systems. (a) We first address the problem of controlling spatiotemporally chaotic systems using a forecast-based feedback control technique. As an example, we suppress turbulent spikes in simulations of the two-dimensional complex …
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Periodic Solutions of Chaotic Partial Differential Equations With Symmetries
… solutions of chaotic partial differential equations with symmetries. Relative time-periodic solutions are solutions which are periodic in time, up to a transformation by an element of the equations' symmetry group. First, we work with the complex Ginzburg-Landau equation (CGLE) as a model …
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Complex Patterns in Extended Oscillatory Systems
… oder raumzeitlichem Chaos werden. Die komplexe Ginzburg-Landau Gleichung (CGLE) stellt ein universelles Modell zur Beschreibung dieser raumzeitlichen Strukturen dar. Diese Arbeit ist der theoretischen Analyse komplexer Muster gewidmet. Mittels numerischer Bifurkations- und Stabilitätsanalyse …