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A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

Part of the Nonlinear Systems and Complexity Book Series (volume 22)

Editors: Macau, Elbert E. N.

DOI: 10.1007/978-3-319-78512-7

ISBN: 978-3-319-78511-0

Publisher: Springer International Publishing - Springer Journals

Jun 15, 2018

1 - 10 of 11 Chapters

Available

From Nonlinear Dynamics to Complex Systems: Introduction

Macau, Elbert E. N.

Pages: 1 –5

[Nonlinear dynamics is about systems whose dynamics is ruled by nonlinear algebraic or nonlinear differential equations. In regard to their physical behavior, the relationships between changes in their inputs and the resultant behavior in their outputs are not proportional to one another. This...
Available

An Overview of the Generalized Gardner Equation: Symmetry Groups and Conservation Laws

Bruzón, M. S.; Gandarias, M. L.; de la Rosa, R.

Pages: 7 –26

[In this paper we study the generalized variable-coefficient Gardner equations of the form ut + A(t)f(u)ux + C(t)f(u)2ux + B(t)uxxx + Q(t)F(u) = 0. This family of equations includes many equations considered in the literature. Some conservation laws are derived by applying the multipliers method....
Available

On Symmetries and Conservation Laws for a Generalized Fisher–Kolmogorov–Petrovsky–Piskunov Equation

Gandarias, María Luz; de los Santos Bruzón, María; Rosa, María

Pages: 27 –50

[This chapter presents a generalized Fisher equation (GFE) from the point of view of the theory of symmetry reductions in partial differential equations. The GFE can be used to describe an ideal growth and spatial-diffusion phenomena. The reductions to ordinary differential equations are derived...
Available

Tunable Orbits Influence in a Driven Stadium-Like Billiard

Livorati, André L. P.

Pages: 51 –67

[The dynamics of a driven stadium-like billiard is investigated through a four-dimensional nonlinear mapping. We set a critical resonance velocity, which plays the role of an ensemble separation according to the initial velocities. When the resonance is active, the invariant curves that surround...
Available

Intermittency and Transport Barriers in Fluids and Plasmas

Chimanski, Emanuel V.; Martins, Caroline G. L.; Chertovskih, Roman; Rempel, Erico L.; Roberto, Marisa; Caldas, Iberê L.; Chian, Abraham C.-L.

Pages: 69 –87

[Leaking chaotic systems represent physical situations in which a hole or leak is introduced in a closed chaotic system. When such a hole is present, trajectories can escape from a trapping region of the phase space and wander for some time, before they return to the first region or settle to a...
Available

An Investigation of the Chaotic Transient for a Boundary Crisis in the Fermi-Ulam Model

Leonel, Edson D.; Marques, Murilo F.

Pages: 89 –108

[Investigation of some statistical properties for a chaotic transient in a Fermi-Ulam model observed after a boundary crisis is considered in this chapter. The crisis is produced by a crossing of a stable and unstable manifold generated from the same saddle fixed point, hence creating also a...
Available

New Trends in Chaos-Based Communications and Signal Processing

Eisencraft, Marcio; Evangelista, João V. C.; Costa, Rafael A.; Fontes, Rodrigo T.; Candido, Renato; Chaves, Daniel P. B.; Pimentel, Cecilio; Silva, Magno T. M.

Pages: 109 –129

[In the last decades many possible applications of nonlinear dynamics in communication systems and signal processing have been reported. Conversely, techniques usually employed by the signal processing and communication systems communities, as correlation, power spectral density analysis, and...
Available

Modeling Fireflies Synchronization

Ramírez-Ávila, Gonzalo Marcelo; Kurths, Jürgen; Depickère, Stéphanie; Deneubourg, Jean-Louis

Pages: 131 –156

[Albeit synchronous behavior of some fireflies species is one of the paradigmatic examples of synchronization, there are not many efforts to model in a realistic way this astounding phenomenon. One of the most important features of fireflies synchronization is the cooperative behavior of many...
Available

From Flocs to Flocks

Algar, Shannon Dee; Stemler, Thomas; Small, Michael

Pages: 157 –175

[In this chapter we present the different ways in which mathematicians think about group formation and group behaviour. We provide an overview of the frameworks that have been borrowed from Physics and discuss their appropriateness and limitations when applied to groups such as a flock of birds....
Available

Network Centrality: An Introduction

Rodrigues, Francisco Aparecido

Pages: 177 –196

[Centrality is a key property of complex networks that influences the behavior of dynamical processes, like synchronization and epidemic spreading, and can bring important information about the organization of complex systems, like our brain and society. There are many metrics to quantify the...

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