Related papers: On Planar Shadowing Curves to Closed Escaping Curv…
We study various weaker forms of inverse shadowing property for discrete dynamical systems on a smooth compact manifold. First, we introduce the so-called Ergodic Inverse Shadowing property (Birhhoff averages of continuous functions along…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
In recent decades, piecewise linear differential systems have attracted considerable attention due to their ability to describe a wide range of phenomena. A central problem, as in the theory of general planar differential systems, is to…
We consider systems of simple closed curves on surfaces and their total number of intersection points, their so-called crossing number. For a fixed number of curves, we aim to minimise the crossing number. We determine the minimal crossing…
The Continuous Polytope Escape Problem (CPEP) asks whether every trajectory of a linear differential equation initialised within a convex polytope eventually escapes the polytope. We provide a polynomial-time algorithm to decide CPEP for…
This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial conditions. The class of…
We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and…
This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a small impact on its statistical behavior. This theoretical…
This paper investigates recurrence properties of dynamical systems under the restriction that control is available only through inputs and outputs. We introduce the concept of ``coarse non-wandering'', a generalization of the classical…
This paper studies a discrete dynamical system belonging to the class of the networks introduced by A.P.~Buslaev. The systems contains a finite set of contours. In any contour, there are cells and a group of particles. This group is called…
Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
Precise motion control of underactuated surface vessels is a crucial task in various maritime applications. In this work, we develop a nonlinear motion control strategy for surface vessels inspired by the pursuit guidance philosophy. Any…
The escape mechanism of the four hill potential is explored. A thorough numerical investigation takes place in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional phase space in…
We study the existence and uniqueness of the time evolution of a system of infinitely many individuals, moving in a tunnel and subjected to a Cucker-Smale type alignment dynamics with compactly supported communication kernels and to…
The dynamics of driven, damped pendulum as used in mechanical clocks is numerically investigated. In addition to the analysis of a well-known mechanisms such as chronometer escapement, the unusual properties of Harrison's grasshopper…
This paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. Three approaches are examined: residual assessment, the method of modified equations, and…
We study deterministic discrete time exclusion type spatially heterogeneous particle processes in continuum. A typical example of this sort is a traffic flow model with obstacles: traffic lights, speed bumps, spatially varying local…
We develop a framework for studying the enhanced dissipation of passive scalars advected by shear flows based on analyzing the particle trajectories of the stochastic differential equation associated with the governing drift-diffusion…
The aim of this work is to revise but also explore even further the escape dynamics in the H\'{e}non-Heiles system. In particular, we conduct a thorough and systematic numerical investigation distinguishing between trapped (ordered and…