Related papers: The Van der Pol Equation
If the duration of the input pulse resonantly interacting with a system is comparable or smaller than the time required for the system to achieve the steady state, transient effects become important. For complex systems, a quantitative…
We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincar\'e surfaces showing return…
Consider quantum harmonic oscillator, perturbed by an even almost-periodic complex-valued potential with bounded derivative and primitive. Suppose that we know the first correction to the spectral asymptotics $\{\Delta\mu_n\}_{n=0}^\infty$…
The paper deals with topical issues of modern mathematical theory of dynamical chaos and its applications. At present, it is customary to assume that dynamical chaos in finitedimensional smooth systems can exist in three different forms.…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
A systematic study of the leading isotropic van der Waals coefficients for the alkali-metal atom + molecule and molecule + molecule systems is presented. Dipole moments and static and dynamic dipole polarizabilities are calculated employing…
We investigate the spectral statistics of chaotic quasi one dimensional systems such as long wires. To do so we represent the spectral correlation function $R(\epsilon)$ through derivatives of a generating function and semiclassically…
Kerr oscillators are model systems which have practical applications in nonlinear optics. Optical Kerr effect i.e. interaction of optical waves with nonlinear medium with polarizability $\chi^{(3)}$ is the basic phenomenon needed to explain…
We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic…
This work explores the intersection of time-delay embeddings, periodic orbit theory, and symbolic dynamics. Time-delay embeddings have been effectively applied to chaotic time series data, offering a principled method to reconstruct…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can…
In this paper, we investigate a calmed version of the 3$D$ rotational Navier-Stokes equations driven by additive noise. First, we use the Ornstein-Uhlenbeck process to transform the equation into a random one. By using the Galerkin…
We observe the occurrence of a strange nonchaotic attractor in a periodically driven two-dimensional map, formerly proposed as a neuron model and a sequence generator. We characterize this attractor through the study of the Lyapunov…
A chaotic attractor is usually characterised by its multifractal spectrum which gives a geometric measure of its complexity. Here we present a characterisation using a minimal set of independant parameters which are uniquely determined by…
This paper extends Yosida's mean ergodic theorem in order to compute projections onto non-unitary eigenspaces for spectral operators of scalar-type on locally convex linear topological spaces. For spectral operators with dominating point…
The dynamics of an oscillator driven by both low- and high- frequency external signals is studied. It is shown that both two- and three-frequency resonances arise due to a nonlinear interaction of these harmonic forces. Conditions which…
We apply periodic orbit theory to a quantum billiard on a torus with a variable number N of small circular scatterers distributed randomly. Provided these scatterers are much smaller than the wave length they may be regarded as sources of…
In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schr\"odinger equation. Our approach is based on periodic perturbations that have the same period as the standing wave…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…