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Article
Dissipative soliton dynamics of the Landau–Lifshitz–Gilbert equation
We study ferromagnetic dissipative systems described by the isotropic LLG equation, from the standpoint of their spatially localized dynamical excitations. In particular, we focus on dissipative soliton s...
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Article
Comparison between the QP formalism and the Painlevé property in integrable dynamical systems
The quasipolynomial (QP) formalism and the Painlevé property constitute two distinct approaches for studying the integrability of systems of ordinary differential equations with polynomial nonlinearities....
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Article
The science of complexity and the role of mathematics
In the middle of the second decade of the 21st century, Complexity Science has reached a turning point. Its rapid advancement over the last 30 years has led to remarkable new concepts, methods and techniques,...
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Article
From mechanical to biological oscillator networks: The role of long range interactions
The study of one-dimensional particle networks of Classical Mechanics, through Hamiltonian models, has taught us a lot about oscillations of particles coupled to each other by nearest neighbor (short range) i...
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Article
Chimera states in a two–population network of coupled pendulum–like elements
More than a decade ago, a surprising coexistence of synchronous and asynchronous behavior called the chimera state was discovered in networks of nonlocally coupled identical phase oscillators. In later years, ...
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Article
The stability of vertical motion in the N-body circular Sitnikov problem
We present results about the stability of vertical motion and its bifurcations into families of 3-dimensional (3D) periodic orbits in the Sitnikov restricted N-body problem. In particular, we consider ν = N − 1 e...
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Chapter and Conference Paper
Global dynamics of coupled standard maps
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Article
Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi–Pasta–Ulam lattices by the Generalized Alignment Index method
The recently introduced GALI method is used for rapidly detecting chaos, determining the dimensionality of regular motion and predicting slow diffusion in multi-dimensional Hamiltonian systems. We propose an e...
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Article
Periodic orbits and bifurcations in the Sitnikov four-body problem
We study the existence, linear stability and bifurcations of what we call the Sitnikov family of straight line periodic orbits in the case of the restricted four-body problem, where the three equal mass primar...
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Article
Stability of motion in the Sitnikov 3-body problem
We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m 1 = m 2 = 0.5) rotating in the x, y plane and vary the mass of...
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Chapter
On The Non-Integrability of the Mixmaster Universe Model
We demonstrate that numerical integration in the complex domain can provide rapidly and efficiently strong evidence on the (non-) integrability of many degree-of-freedom systems, which is particularly useful i...
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Article
Synchronization in parametrically driven Hamiltonian systems
Analytical and numerical techniques of non-linear dynamics are used to study synchronization in certain periodically modulated 2-dimensional Hamiltonian systems. Our model equation describes the behaviour of a...
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Book
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Book
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Chapter
Fluxon Dynamics in Single and Coupled Long Josephson Junctions With Inhomogeneities
Fluxon dynamics in a variety of Long Josephson Junction CLJJ) systems is studied using the collective coordinate analysis of McLaughlin and Scott, and the results of the ODE predictions are compared with the n...
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Article
Chaos in nonlinear paradoxical games
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Article
Chaos in nonlinear paradoxical games
Paradoxical games are nonconstant sum conflicts, where individual and collective rationalities are at variance and refer to a dyadic antagonism where the contestants blackmail each other. The state space dynam...
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Chapter and Conference Paper
A Singularity Analysis Approach to the Solutions of Duffing’s Equation
The singularity structure of Duffing’s equation in the complex t-plane is investigated analytically and numerically. A series expansion for the general solution around each singularity t* = tR+itI is given, and i...
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Article
Is the Hamiltonian \(H = (\dot x^2 + \dot y^2 + x^2 y^2 )/2\) completely chaotic?completely chaotic?
By following the bifurcation sequences of two main families of periodic orbits of the Hamiltonian $$H(\alpha ) = (\dot x^2 + \dot y^...
