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Chapter and Conference Paper
Dynamics and Statistics of Weak Chaos in a 4-D Symplectic Map
The important phenomenon of “stickiness” of chaotic orbits in low dimensional dynamical systems has been investigated for several decades, in view of its applications to various areas of physics, such as class...
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Book and Conference Proceedings
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Article
Energy transport in one-dimensional oscillator arrays with hysteretic dam**
Energy transport in one-dimensional oscillator arrays has been extensively studied to date in the conservative case, as well as under weak viscous dam**. When driven at one end by a sinusoidal force, such ar...
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Article
Open AccessThe Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport
We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist fi...
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Article
Complex statistics in Hamiltonian barred galaxy models
We use probability density functions (pdfs) of sums of orbit coordinates, over time intervals of the order of one Hubble time, to distinguish weakly from strongly chaotic orbits in a barred galaxy model. We fi...
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Book
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Chapter
Hamiltonian Systems of Few Degrees of Freedom
In Chap. 2 we provide first an elementary introduction to some simple examples of Hamiltonian systems of one and two degrees of freedom. We describe the essential features of phase space plots and focus on the...
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Chapter
Normal Modes, Symmetries and Stability
The present Chapter studies nonlinear normal modes (NNMs) of coupled oscillators from an altogether different perspective. Focusing entirely on periodic boundary conditions and using the Fermi Pasta Ulam β (FP...
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Chapter
FPU Recurrences and the Transition from Weak to Strong Chaos
The present Chapter starts with a historical introduction to the FPU one-dimensional lattice as it was first integrated numerically by Fermi Pasta and Ulam in the 1950s and describes the famous paradox of the ...
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Chapter
The Statistical Mechanics of Quasi-stationary States
This Chapter adopts an altogether different approach to the study of chaos in Hamiltonian systems. We consider, in particular, probability distribution functions (pdfs) of sums of chaotic orbit variables in di...
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Chapter
Introduction
Chapter 1 starts by defining a dynamical system in terms of ordinary differential equations and presents the fundamental framework within which one can study the stability of their equilibrium (or fixed) point...
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Chapter
Local and Global Stability of Motion
In this Chapter, we discuss in a unified way equilibrium points, periodic orbits and their stability, which constitute local concepts of Hamiltonian dynamics together with ordered and chaotic motion, which are th...
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Chapter
Efficient Indicators of Ordered and Chaotic Motion
This Chapter opens with an introduction to the variational equations, derived by the linearization of the ordinary differential equations of a Hamiltonian system, and the equations of the tangent map, obtained by...
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Chapter
Localization and Diffusion in Nonlinear One-Dimensional Lattices
In this Chapter we focus on localization properties of nonlinear lattices in the configuration space of their spatial coordinates. In particular, we begin by discussing the phenomenon of exponentially localize...
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Chapter
Conclusions, Open Problems and Future Outlook
The final Chapter first summarizes and discusses the main conclusions described in the book. We then list a number of open problems, which we feel should be further pursued in continuation of what we have pres...
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Chapter and Conference Paper
Model Reduction of a Higher-Order KdV Equation for Shallow Water Waves
We present novel results on a non-integrable generalized KdV equation proposed by Fokas [A.S. Fokas, Physica D87, 145 (1995)], aiming to describe unidirectional solitary water waves with greater accuracy than ...
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Article
Chaos synchronization of two different chaotic complex Chen and Lü systems
This paper investigates the phenomenon of chaos synchronization of two different chaotic complex systems of the Chen and Lü type via the methods of active control and global synchronization. In this regard, it ge...
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Article
Open AccessThe Shape of Soliton-Like Solutions of a Higher-Order Kdv Equation Describing Water Waves
We study the solitary wave solutions of a non-integrable generalized KdV equation proposed by Fokas [A. S. Fokas, Physica D 87, 145 (1995)], aiming to describe unidirectional waves in shallow water with greater a...
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Chapter
Discrete Breathers in Nonlinear Lattices: A Review and Recent Results
Localization phenomena in systems of many (often infinite) degrees of freedom have attracted attention in solid state physics, nonlinear optics, superconductivity and quantum mechanics. The type of localizatio...
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Article
Anomalous Statistics for Type-III Intermittency
The statistics for the distribution of laminar phases in type-IIIintermittency is examined for the map $$x_{n + 1} = - ((1 + \mu )x...
