Related papers: The developing structure of dynamical systems
The border-collision normal form is a piecewise-linear family of continuous maps that describe the dynamics near border-collision bifurcations. Most prior studies assume each piece of the normal form is invertible, as is generic from an…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…
In this paper, we consider sufficient conditions for an invariant double circle to occur in a one parameter discrete dynamical systems on a cylinder.
We study the cosmological dynamics of non-minimally coupled matter models using the Brown's variational approach to relativistic fluids in General Relativity. After decomposing the Ricci scalar into a bulk and a boundary term, we construct…
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. We will give a brief overview about important and…
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…
The existence of multiple radial solutions to the elliptic equation modeling fermionic cloud of interacting particles is proved for the limiting Planck constant and intermediate values of mass parameters. It is achieved by considering the…
The impact of quenched disorder on deterministic diffusion in chaotic dynamical systems is studied. As a simple example, we consider piecewise linear maps on the line. In computer simulations we find a complicated scenario of multiple…
In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time--dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a…
This paper attempts to make feasible the evolutionary emergence of novelty in a supposedly deterministic world which behavior is associated with those of the mathematical dynamical systems. The work was motivated by the observation of…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerical continuation and numerical solutions methods. Regarding numerical solution methods, its dynamics is characterized on Lyapunov and isoperiodic…
Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…