Related papers: A multi-dimensional-time dynamical system
Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the…
We investigate the dynamical system generated by the function $\lfloor\lambda x\rfloor$ defined on $\mathbb R$ and with a parameter $\lambda\in \mathbb R$. For each given $m\in \mathbb N$ we show that there exists a region of values of…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
In this paper, we study Random Dynamical Systems (RDSs) of homeomorphisms on the circle without a finite orbit. We characterize the topological dynamics of the associated semigroup by identifying the existence of invariant sets which are…
In this article, we study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when…
In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
Dynamical Systems is a field that studies the collective behavior of objects that update their states according to some rules. Discrete-time Boolean Finite Dynamical System (DT-BFDS) is a subfield where the systems have some finite number…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…
In this paper, we examine a specific class of quadratic operators. For these operators, we identified all fixed points and categorized their types in the general case. Our analysis revealed that there are no attractive fixed points except…
Time series datasets are often composed of a variety of sequences from the same domain, but from different entities, such as individuals, products, or organizations. We are interested in how time series models can be specialized to…
In this article, a novel Finite Time Stability (FTS) analysis of Fractional-Order Time Delay Systems (FOTDSs) is proposed. By using the fixed point approach, sufficient conditions for the robust FTS of FOTDSs have been established. Two…
With the rapid development of more complex robots, Fault Detection and Diagnosis (FDD) becomes increasingly harder. Especially the need for predetermined models and historic data is problematic because they do not encompass the dynamic and…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Recently, continuous-time dynamical systems, based on systems of ordinary differential equations, for mosquito populations are studied. In this paper we consider discrete-time dynamical system generated by an evolution quadratic operator of…
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given…