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Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments
Vadim S. Anishchenko Vladimir Astakhov Tatjana Vadivasova Alexander Neiman Lutz Schimansky-Geier
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| Institución detectada | Año de publicación | Navegá | Descargá | Solicitá |
|---|---|---|---|---|
| No detectada | 2007 | SpringerLink |
Información
Tipo de recurso:
libros
ISBN impreso
978-3-540-38164-8
ISBN electrónico
978-3-540-38168-6
Editor responsable
Springer Nature
País de edición
Reino Unido
Fecha de publicación
2007
Información sobre derechos de publicación
© Springer 2007
Cobertura temática
Tabla de contenidos
Tutorial
Vadim S. Anishchenko; Vladimir Astakhov; Tatjana Vadivasova; Alexander Neiman; Lutz Schimansky-Geier
The knowledge of nonlinear dynamics is based on the notion of a dynamical system (DS). A DS may be thought of as an object of any nature, whose state evolves in time according to some dynamical law, i.e., as a result of the action of a deterministic evolution operator. Thus, the notion of DS is the result of a certain amount of idealization when random factors inevitably present in any real system are neglected.
Palabras clave: Lyapunov Exponent; Phase Portrait; Unstable Manifold; Chaotic Attractor; Langevin Equation.
Pp. 1-108
Dynamical Chaos
Vadim S. Anishchenko; Vladimir Astakhov; Tatjana Vadivasova; Alexander Neiman; Lutz Schimansky-Geier
A dynamical system (DS) displays its nonlinear properties in different ways with variation of system control parameters. An increase in the influence of nonlinearity causes the dynamical regime to become complicated. Simple attractors in the phase space of a dissipative system are replaced by more complicated ones. Under certain conditions, nonlinearity can lead to the onset of dynamical chaos. Moving along a relevant direction in parameter space, one can observe a set of bifurcations resulting in the appearance of a chaotic attractor. Such typical bifurcation sequences are called the bifurcation mechanisms , or the scenarios of the transition to chaos .
Palabras clave: Lyapunov Exponent; Phase Portrait; Chaotic Attractor; Phase Trajectory; Chaos Synchronization.
Pp. 109-306
Stochastic Dynamics
Vadim S. Anishchenko; Vladimir Astakhov; Tatjana Vadivasova; Alexander Neiman; Lutz Schimansky-Geier
The word “noise” is ordinarily associated with the term “hindrance”. It was traditionally considered that the presence of noise can only make the operation of any system worse. There are well-known classical radio physical problems related to limitations of the sensitivity of amplifiers and a finiteness of the pulse bandwidth of oscillators due to the presence of natural and technical noise [1–3] (cf. Sect. 1.3).
Palabras clave: Noise Intensity; Stochastic Resonance; Stochastic Dynamics; Bistable System; Linear Response Theory.
Pp. 307-443