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math.DS2018
Asymptotics of the heat kernels on 2D lattices
Pavel Gurevich
We obtain asymptotic expansions of the spatially discrete 2D heat kernels, or Green's functions on lattices, with respect to powers of time variable up to an arbitrary order and es…
math.DS2017
Pulses in FitzHugh--Nagumo systems with rapidly oscillating coefficients
Pavel Gurevich, Sina Reichelt
This paper is devoted to pulse solutions in FitzHugh--Nagumo systems that are coupled parabolic equations with rapidly periodically oscillating coefficients. In the limit of vanish…
math.DS2016
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…