Related papers: Periodicity Analysis of the Logistic Map over Ring…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
We study the problem of patrolling the nodes of a network collaboratively by a team of mobile agents, such that each node of the network is visited by at least one agent once in every $I(n)$ time units, with the objective of minimizing the…
Periodicity and relaxation are investigated for the trajectories of the states in cylindrical linear cellular automata. The time evolutions are described with matrices. The eigenvalue analysis is applied to obtain the maximum values of…
The problem of finding the longest simple cycle in a directed graph is NP-hard, with critical applications in computational biology, scheduling, and network analysis. Existing approaches include exact algorithms with exponential runtimes,…
We study the dynamics of a piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in $\mathbb{R}^2$. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each…
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…
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…
We develop a sequential-topological study of rational points of schemes of finite type over local rings typical in higher dimensional number theory and algebraic geometry. These rings are certain types of multidimensional complete fields…
Coupled map lattices have been widely used as models in several fields of physics, such as chaotic strings, turbulence, and phase transitions, as well as in other disciplines, such as biology (ecology, evolution) and information processing.…
Periodic orbits are fundamental to understand the dynamics of nonlinear systems. In this work, we focus on two aspects of interest regarding periodic orbits, in the context of a dissipative mapping, derived from a prototype model of a…
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…
We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the…
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself…
Parallel real-time systems (e.g., autonomous driving systems) often contain functionalities with complex dependencies and execution uncertainties, leading to significant timing variability which can be represented as a probabilistic…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
Logistics and transportation networks require a large amount of resources to realize necessary connections between locations and minimizing these resources is a vital aspect of planning research. Since such networks have dynamic connections…
A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
In the graph exploration problem, a team of mobile computational entities, called agents, arbitrarily positioned at some nodes of a graph, must cooperate so that each node is eventually visited by at least one agent. In the literature, the…