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As periodic orbit theory works badly on computing the observable averages of dynamical systems with intermittency, we propose a scheme to cooperate with cycle expansion and perturbation theory so that we can deal with intermittent systems…
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions, we use basic tools of ordinary differential equations to…
A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…
A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular-chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence…
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…
We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…
Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated…
This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…
Coupled Tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics, using the stochastic quantisation of Parisi and Wu. This paper studies dynamical properties of these maps, finding…
Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…
A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off…
We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index…
DDEBIFTOOL is a collection of Matlab routines for numerical bifurcation analysis of systems of delay differential equations with discrete constant and state-dependent delays. The package supports continuation and stability analysis of…
This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. This paper outlines the stability analysis and a procedure to reduce and simplify the non-linear…
In this paper, we investigate the Rayleigh-Taylor instability problem for two compressible, immiscible, inviscid flows rotating with an constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
This paper generalizes a previously-conceived, continuation-based optimization technique for scalar objective functions on constraint manifolds to cases of periodic and quasiperiodic solutions of delay-differential equations. A Lagrange…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…
In this paper some piecewise smooth perturbations of a three-dimensional differential system are considered. The existence of invariant manifolds filled by periodic orbits is obtained after suitable small perturbations of the original…