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The order and chaos of the motion near equilibrium points in the potential of a rotating highly irregular-shaped celestial body are investigated from point of view of the dynamical system theory. The positions of the non-degenerate…
This paper describes a predictive control method to search for unstable periodic orbits of the generalized tent map. The invariant set containing periodic orbits is a repelling set with a complicated Cantor-like structure. Therefore, a…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…
The Fisher-Shannon complexity plane is a powerful tool that represents complex dynamics in a two-dimensional plane. It locates a dynamical system based upon its entropy and its Fisher Information Measure (FIM). It has been recently shown…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
A competitive resource-consumer dynamical model is analyzed based on an integrated model of a competitive Lotka-Volterra model and a prey-predator Rosenzweig-MacArthur model that we call that LV-RM model throughout this paper. Resource…
The Oriented Associativity equation plays a fundamental role in the theory of Integrable Systems. In this paper we prove that the equation, besides being Hamiltonian with respect to a first-order Hamiltonian operator, has a third-order…
Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…
We test numerically the recently proposed linear relationship between the scale-invariant period $T_{\rm s.i.} = T |E|^{3/2}$, and the topology of an orbit, on several hundred planar Newtonian periodic three-body orbits. Here $T$ is the…
Furstenberg--Zimmer structure theory refers to the extension of the dichotomy between the compact and weakly mixing parts of a measure preserving dynamical system and the algebraic and geometric descriptions of such parts to a conditional…
Often topological classes of one-dimensional dynamical systems are finite codimension smooth manifolds. We describe a method to prove this sort of statement that we believe can be applied in many settings. In this work we will implement it…
We study the descriptive complexity of sets of points defined by placing restrictions on statistical behaviour of their orbits in dynamical systems on Polish spaces. A particular examples of such sets are the set of generic points of a…
A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially…
Inspired by Katok's intermediate entropy property [Inst. Hautes \'Etudes Sci. Publ. Math. 51 (1980), 137-173], we introduce and study the notion of entropy flexibility for discrete-time and continuous-time dynamical systems. By using…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity is encoded in the time between oscillations of the norm,…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier--Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a…
We give a concrete method to explicitly compute the rational cohomology of the unordered configuration spaces of connected, oriented, closed, even-dimensional manifolds of finite type which we have implemented in Sage [S+09]. As an…