64 citations · 501 across the 30 of their papers we have counts for
17 papers · 1 filter
St. Petersburg paradox for quasiperiodically hypermeandering spiral waves
Vadim N. Biktashev, Ian Melbourne
It is known that quasiperiodic hypermeander of spiral waves almost certainly produces a bounded trajectory for the spiral tip. We analyse the size of this trajectory. We show that…
Exact Propagating Wave Solutions in Reaction Cross-Diffusion System
Abdullah Aldurayhim, Vadim N. Biktashev
Reaction-diffusion systems with cross-diffusion terms in addition to, or instead of, the usual self-diffusion demonstrate interesting features which motivate their further study. T…
Predicting critical ignition in slow-fast excitable models
Christopher D. Marcotte, Vadim N. Biktashev
Linearization around unstable travelling waves in excitable systems can be used to approximate strength-extent curves in the problem of initiation of excitation waves for a family…
A response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves
Hans Dierckx, Alexander V. Panfilov, Henri Verschelde +2
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral w…
Fast-slow asymptotics for a Markov chain model of fast sodium current
T. Stary, V. N. Biktashev
We explore the feasibility of using fast-slow asymptotic to eliminate the computational stiffness of the discrete-state, continuous-time deterministic Markov chain models of ionic…
Strength-Duration Relationship in an Excitable Medium
B. Bezekci, V. N. Biktashev
We consider the strength-duration relationship in one-dimensional spatially extended excitable media. In a previous study [Idris and Biktashev 2008] set out to separate initial (or…