18 citations · 18 across the 5 of their papers we have counts for
5 papers
From two-dimensional continuous maps to one-dimensional discontinuous maps: a novel reduction explaining complex bifurcation structures in piecewise-linear families of maps
D. J. W. Simpson, V. Avrutin
Piecewise-linear maps describe dynamical phenomena that switch between distinct states and readily generate complex bifurcation structures due to their strong nonlinearity. We show…
Doubling bifurcations of invariant closed curves in 3D maps
Sayanho Biswas, Soumitro Banerjee, Viktor Avrutin +1
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…
Bistability in a one-dimensional model of a two-predators-one-prey population dynamics system
Sergey Kryzhevich, Viktor Avrutin, Gunnar Söderbacka
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-dimension…
Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps
Sergey Kryzhevich, Viktor Avrutin, Nikita Begun +2
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…
The Role of Constraints in a Segregation Model: The Symmetric Case
D. Radi, L. Gardini, V. Avrutin
In this paper we study the effects of constraints on the dynamics of an adaptive segregation model introduced by Bischi and Merlone (2011). The model is described by a two dimensio…