Search results for "dynamical systems theory"
showing 10 items of 126 documents
Anharmonic effects on the dynamic behavior’s of Klein Gordon model’s
2021
Abstract This work completes and extends the Ref. Tchakoutio Nguetcho et al. (2017), in which we have focused our attention only on the dynamic behavior of gap soliton solutions of the anharmonic Klein-Gordon model immersed in a parameterized on-site substrate potential. We expand our work now inside the permissible frequency band. These considerations have crucial effects on the response of nonlinear excitations that can propagate along this model. Moreover, working in the allowed frequency band is not only interesting from a physical point of view, it also provides an extraordinary mathematical model, a new class of differential equations possessing vital parameters and vertical singular …
Stability and Chaos
2010
In this chapter we study a larger class of dynamical systems that include but go beyond Hamiltonian systems. We are interested, on the one hand, in dissipative systems, i.e. systems that lose energy through frictional forces or into which energy is fed from exterior sources, and, on the other hand, in discrete, or discretized, systems such as those generated by studying flows by means of the Poincare mapping. The occurence of dissipation implies that the system is coupled to other, external systems, in a controllable manner. The strength of such couplings appears in the set of solutions, usually in the form of parameters. If these parameters are varied it may happen that the flow undergoes …
Nondegeneracy in the Perturbation Theory of Integrable Dynamical Systems
1990
The most general nondegeneracy condition for the existence of invariant tori in nearly integrable and analytic Hamiltonian systems is formulated.
Nearly-integrable dissipative systems and celestial mechanics
2010
The influence of dissipative effects on classical dynamical models of Celestial Mechanics is of basic importance. We introduce the reader to the subject, giving classical examples found in the literature, like the standard map, the Hénon map, the logistic mapping. In the framework of the dissipative standard map, we investigate the existence of periodic orbits as a function of the parameters. We also provide some techniques to compute the breakdown threshold of quasi-periodic attractors. Next, we review a simple model of Celestial Mechanics, known as the spin-orbit problem which is closely linked to the dissipative standard map. In this context we present the conservative and dissipative KA…
The influence of the solvent's mass on the location of the dividing surface for a model Hamiltonian
2019
The Transition State dividing surface is a key concept, not only for the precise calculation of the rate constant of a reaction, but also for the proper prediction of product ratios. The correct location of this surface is defined by the requirement that reactive trajectories do not recross it. In the case of reactions in solution the solvent plays an important role in the location of the dividing surface. In this paper we show with the aid of a model Hamiltonian that the effective mass of the solvent can dramatically change the location of the dividing surface. Keywords: Dynamical systems, Dividing surface, Reactions in solution, 2019 MSC: 00-01, 99-00
Bifurcations of phase portraits of a Singular Nonlinear Equation of the Second Class
2014
Abstract The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non-convex interparticle interactions immersed in a parameterized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Non-convex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. In the continuum limit for such a model, the particles are governed by a Singular Nonlinear Equation of the Second Class. The dynamical behavior of traveling wave solutions is studied by using the theory of bifurcations of dynamical systems. Under different para…
Perturbations of the classical Lotka-Volterra system by behavioral sequences
1995
The complexity and the variability of parameters occurring in ecological dynamical systems imply a large number of equations.
Group Foundations of Quantum and Classical Dynamics : Towards a Globalization and Classification of Some of Their Structures
1987
This paper is devoted to a constructiveand critical analysis of the structure of certain dynamical systems from a group manifold point of view recently developed. This approach is especially suitable for discussing the structure of the quantum theory, the classical limit, the Hamilton-Jacobi theory and other problems such as the definition and globalization of the Poincare-Cartan form which appears in the variational approach to higher order dynamical systems. At the same time, i t opens a way for the classification of all hamiltonian and lagrangian systems associated with suitably defined dynamical groups. Both classical and quantum dynamics are discussed, and examples of all the different…
Quasienergy states of trapped ions
2000
The quantum models for a single trapped ion are extended to the description of the collective dynamics for systems of ions confined in quadrupole electromagnetic traps with cylindrical symmetry. A class of quantum Hamiltonians with suitable axial and radial interaction potentials given by homogeneous functions of degree (-2) and invariant under translations and axial rotations are introduced. The considered axial and radial quantum Hamiltonians for the center-of-mass and relative motions are described by collective dynamical systems associated to the symplectic group \(\). Discrete quasienergy spectra are obtained and the corresponding quasienergy states are explicitly realized as \(\) cohe…
Hidden Oscillations In The Closed-Loop Aircraft-Pilot System And Their Prevention* *This work was supported by Russian Science Foundation (project 14…
2016
Abstract The paper is devoted to studying and prevention of a special kind of oscillations-the Pilot Involved Oscillations (PIOs) which may appear in man-machine closed-loop dynamical systems. The PIO of categories II and III are defined as essentially non-linear unintended steady fluctuations of the piloted aircraft, generated due to pilot efforts to control the aircraft with a high precision. The main non-linear factor leading to the PIO is, generally, rate limitations of the aircraft control surfaces, resulting in a delay in the response of the aircraft to pilot commands. In many cases, these oscillations indicate presence of hidden, rather than self-excited attractors in the aircraft-pi…