46 citations · 102 across the 26 of their papers we have counts for
17 papers · 1 filter
Global stability of SIR model with heterogeneous transmission rate modeled by the Preisach operator
Ruofei Guan, Jana Kopfová, Dmitrii Rachinskii
In recent years, classical epidemic models, which assume stationary behavior of individuals, have been extended to include an adaptive heterogeneous response of the population to t…
Dynamics of SIR model with heterogeneous response to intervention policy
Dmitrii Rachinskii, Samiha Rouf
We study dynamics of a variant of the SIR the model, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by th…
A deterministic model for non-monotone relationship between translation of upstream and downstream open reading frames
D. E. Andreev, P. V. Baranov, A. Milogorodskii +1
TASEP modeling was shown to offer a parsimonious explanation for the experimentally confirmed ability of a single upstream Open Reading Frames (uORFs) to upregulate downstream tran…
Effect of diagnostic testing on the isolation rate in a compartmental model with asymptomatic groups
Zuzana Chladná, Jana Kopfová, Dmitrii Rachinskii +1
We present two epidemiological models, which extend the classical SEIR model by accounting for the effect of indiscriminate quarantining, isolation of infected individuals based on…
Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator
Jana Kopfová, Petra Nábělková, D. Rachinskii +1
We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled…
Guaranteed estimates for the length of branches of periodic orbits for equivariant Hopf bifurcation
E. Hooton, Z. Balanov, D. Rachinskii
Connected branches of periodic orbits originating at a Hopf bifurcation point of a differential system are considered. A computable estimate for the range of amplitudes of periodic…
Mixed global dynamics of forced vibro-impact oscillator with Coulomb friction
Oleg Gendelman, Pavel Kravetc, Dmitrii Rachinskii
The paper revisits a well-known model of forced vibro-impact oscillator with Amonton-Coulomb friction. In vast majority of the existing studies, this model included also viscous fr…
A continuum of path-dependent equilibrium solutions induced by sticky expectations
Pavel Krejci, Eyram Kwame, Harbir Lamba +1
We analyze a simple macroeconomic model where rational inflation expectations is replaced by a boundedly rational, and genuinely sticky, response to changes in the actual inflation…
Global stability of a piecewise linear macroeconomic model with a continuum of equilibrium states and sticky expectation
Pavel Krejci, Harbir Lamba, Dmitrii Rachinskii
We consider piecewise linear discrete time macroeconomic models, which possess a continuum of equilibrium states. These systems are obtained by replacing rational inflation expecta…
Chaos in Saw Map
Nikita Begun, Pavel Kravetc, Dmitrii Rachinskii
We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such maps are generated as a Poincaré map of simple two-dimensional…
Hopf Bifurcation of Relative Periodic Solutions: Case Study of a Ring of Passively Mode-Locked Lasers
Zalman Balanov, Pavel Kravetc, Wieslaw Krawcewicz +1
In this paper, we consider an equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in systems of functional differential equations respecting $Γ\tim…
Equivariant Versions of Odd Number Theorem
Edward Hooton, Pavel Kravetc, Dmitrii Rachinskii
We consider the problem of stabilization of unstable periodic solutions to autonomous systems by the non-invasive delayed feedback control known as Pyragas control method. The Odd…
On geometric conditions for reduction of the Moreau sweeping process to the Prandtl-Ishlinskii operator
D. Rachinskii
The sweeping process was proposed by J. J. Moreau as a general mathematical formalism for quasistatic processes in elastoplastic bodies. This formalism deals with connected Prandtl…
Dynamics of Discrete Time Systems with a Hysteresis Stop Operator
Maxim Arnold, Nikita Begun, Pavel Gurevich +3
We consider a piecewise linear two-dimensional dynamical system that couples a linear equation with the so-called stop operator. Global dynamics and bifurcations of this system are…
Pulsating dynamics of slow-fast population models with delay
Pavel Kravetc, Dmitrii Rachinskii, Andrei Vladimirov
We discuss a bifurcation scenario which creates periodic pulsating solutions in slow-fast delayed systems through a cascade of almost simultaneous Hopf bifurcations. This scenario…
Realization of Arbitrary Hysteresis by a Low-dimensional Gradient Flow
Dmitrii Rachinskii
We consider gradient systems with an increasing potential that depends on a scalar parameter. As the parameter is varied, critical points of the potential can be eliminated or crea…
Blow Up of a Cycle in Lotka-Volterra Type Equations with Competition-Cooperation Terms and Quasi-Linear Systems
E. Bouse, D. Rachinskii
We consider systems where a cycle born via the Hopf bifurcation blows up to infinity as a parameter ranges over a finite interval. Two examples demonstrating this effect are presen…