180 citations · 1.3k across the 65 of their papers we have counts for
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Traveling wave solutions in the Burridge-Knopoff model
C. B. Muratov
The slider-block Burridge-Knopoff model with the Coulomb friction law is studied as an excitable medium. It is shown that in the continuum limit the system admits solutions in the…
Theory of Spike Spiral Waves in a Reaction-Diffusion System
C. B. Muratov, V. V. Osipov
We discovered a new type of spiral wave solutions in reaction-diffusion systems --- spike spiral wave, which significantly differs from spiral waves observed in FitzHugh-Nagumo-typ…
Spike autosolitons in the Gray-Scott model
C. B. Muratov, V. V. Osipov
We performed a comprehensive study of the spike autosolitons: self-sustained solitary inhomogeneous states, in the classical reaction-diffusion system --- the Gray-Scott model. We…
Synchronization, chaos, and breakdown of collective domain oscillations in reaction-diffusion systems
C. B. Muratov
The universal equations describing collective oscillations of the multidomain patterns of small period in an arbitrary -dimensional reaction-diffusion system of the activator-in…
Scenarios of domain pattern formation in a reaction-diffusion system
C. B. Muratov, V. V. Osipov
We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both mult…
Self-replication and splitting of domain patterns in reaction-diffusion systems with fast inhibitor
C. B. Muratov
An asymptotic equation of motion for the pattern interface in the domain-forming reaction-diffusion systems is derived. The free boundary problem is reduced to the universal equati…