32 citations · 96 across the 34 of their papers we have counts for
12 papers · 1 filter
Existence and stability of a limit cycle in the model of a planar passive biped walking down a slope
Oleg Makarenkov
We consider the simplest model of a passive biped walking down a slope given by the equations of switched coupled pendula (McGeer, 1990). Following the fundamental work by Garcia e…
Structurally stable families of periodic solutions in sweeping processes of networks of elastoplastic springs
Ivan Gudoshnikov, Oleg Makarenkov
Networks of elastoplastic springs (elastoplastic systems) have been linked to differential equations with polyhedral constraints in the pioneering paper by Moreau (1974). Periodic…
Global asymptotic stability of nonconvex sweeping processes
Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov, Oleg Makarenkov
Building upon the technique that we developed earlier for perturbed sweeping processes with convex moving constraints and monotone vector fields (Kamenskii et al, Nonlinear Anal. H…
A continuation principle for periodic BV-continuous state-dependent sweeping processes
Mikhail Kamenskii, Oleg Makarenkov, Lakmi Niwanthi Wadippuli
We consider a Caratheodory differential equation with a state-dependent convex constraint that changes BV-continuously in time (a perturbed BV-continuous state-dependent sweeping p…
Bifurcations of finite-time stable limit cycles from focus boundary equilibria in impacting systems, Filippov systems and sweeping processes
Oleg Makarenkov, Lakmi Niwanthi Wadippuli
We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove bifurcation of limit cycles…
Bifurcation of limit cycles from a switched equilibrium in planar switched systems and its application to power converters
Oleg Makarenkov
We consider a switched system of two subsystems that are activated as the trajectory enters the regions and respectively, where …
Dwell time for local stability of switched systems with application to non-spiking neuron models
Oleg Makarenkov, Anthony Phung
For switched systems that switch between distinct globally stable equilibria, we offer closed-form formulas that lock oscillations in the required neighborhood of the equilibria. M…
Global stability of almost periodic solutions of monotone sweeping processes and their response to non-monotone perturbations
Mikhail Kamenskii, Oleg Makarenkov, Lakmi Niwanthi +1
We develop a theory which allows making qualitative conclusions about the dynamics of both monotone and non-monotone Moreau sweeping processes. Specifically, we first prove that an…
Dwell time for switched systems with multiple equilibria on a finite time-interval
Oleg Makarenkov, Anthony Phung
We describe the behavior of solutions of switched systems with multiple globally exponentially stable equilibria. We introduce an ideal attractor and show that the solutions of the…
A new test for stick-slip limit cycles in dry-friction oscillators with small nonlinear friction characteristics
O. Makarenkov
We consider a dry friction oscillator on a moving belt with both the Coulomb friction and a small nonlinear addition which can model e.g. the Stribeck effect. By using the perturba…
Bifurcation of limit cycles from a fold-fold singularity in planar switched systems
Oleg Makarenkov
An anti-lock braking system (ABS) is the primary motivation for this research. The ABS controller switches the actions of charging and discharging valves in the hydraulic actuator…
Degenerate resonances and their stability in planar systems with small negative divergence
O. Yu. Makarenkov, I. S. Martynova
We consider a conservative system with small periodic perturbations under the assumption that the divergence of the perturbed system is negative. The main theorems provide universa…