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math.DS2024
Perfect stationary solutions of reaction-diffusion equations on lattices and regular graphs
Vladimír Švígler, Jonáš Volek
Reaction-diffusion equations on infinite graphs can have an infinite number of stationary solutions. These solutions are generally described as roots of a countable system of algeb…
math.DS2020
Periodic stationary solutions of the Nagumo lattice differential equation: existence regions and their number
Vladimír Švígler
The Nagumo lattice differential equation admits stationary solutions with arbitrary spatial period for sufficiently small diffusion rate. The continuation from the stationary solut…
math.DS2018
On Arbitrarily Long Periodic Orbits of Evolutionary Games on Graphs
Jeremias Epperlein, Vladimír Švígler
A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavi…