arXiv subjects

Viktor Avrutin

Publications and source records attributed to Viktor Avrutin.

4 recordsLinked to original sources

arXiv2025

Doubling bifurcations of invariant closed curves in 3D maps

Numerous studies have reported two types of doubling of invariant closed curves (ICCs) in dynamical systems: (a) the creation of two disjoint ICCs such that iterations flip between them; and (b) the creation of a single ICC of double the length of the original ICC. Various methods have been proposed to analyze such bifurcations. We show that the methods proposed so far are not always adequate for analyzing and predicting these bifurcations. We propose a new method to overcome the difficulties.

math.DS↗

arXiv2024

Do We Run Large-scale Multi-Robot Systems on the Edge? More Evidence for Two-Phase Performance in System Size Scaling

With increasing numbers of mobile robots arriving in real-world applications, more robots coexist in the same space, interact, and possibly collaborate. Methods to provide such systems with system size scalability are known, for example, from swarm robotics. Example strategies are self-organizing behavior, a strict decentralized approach, and limiting the robot-robot communication. Despite applying such strategies, any multi-robot system breaks above a certain critical system size (i.e., number of robots) as too many robots share a resource (e.g., space, communication channel). We provide additional evidence based on simulations, that at these critical system sizes, the system performance separates into two phases: nearly optimal and minimal performance. We speculate that in real-world applications that are configured for optimal system size, the supposedly high-performing system may actually live on borrowed time as it is on a transient to breakdown. We provide two modeling options (based on queueing theory and a population model) that may help to support this reasoning.

cs.RO↗

arXiv2021

Bistability in a one-dimensional model of a two-predators-one-prey population dynamics system

In this paper, we study the classical two-predators-one-prey model. The classical model described by a system of 3 ordinary differential equations can be reduced to a one-dimensional bimodal map. We prove that this map has at most two stable periodic orbits. Besides, we describe the structure of bifurcations of the map. Taking this mechanism into account, one can easily detect parameter regions where cycles with arbitrary high periods or chaotic attractors with arbitrary high numbers of bands coexist pairwise.

math.DS↗

arXiv2021

Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear~naturally.

math.DS↗