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We consider a spatially distributed population dynamics model with excitable predator-prey kinetics, where species propagate in space due to their taxis with respect to each other's gradient in… (More)

We consider a system of partial differential equations describing two spatially distributed populations in a “predator-prey” interaction with each other. The spatial evolution is governed by three… (More)

- K. I. Agladze, L Budriene, Genrih Romanovitch Ivanitsky, Valentin Krinsky, V Shakhbazyan, Mikhail A Tsyganov
- Proceedings. Biological sciences
- 1993

The occurrence of spatially ordered structures plays an important role in biology (examples: morphogenesis, ecosystems, dynamics of populations, etc.). Turing proposed a reaction-diffusion process… (More)

- Kate Byrne, Naser Monsefi, +14 authors Boris N. Kholodenko
- Cell systems
- 2016

Dynamic interactions between RhoA and Rac1, members of the Rho small GTPase family, play a vital role in the control of cell migration. Using predictive mathematical modeling, mass spectrometry-based… (More)

- Mikhail A Tsyganov, Walter Kolch, Boris N. Kholodenko
- Molecular bioSystems
- 2012

Small monomeric G-proteins control cellular behavior, cycling between inactive GDP-bound and active GTP-bound states. Activating and deactivating transitions are regulated by guanine nucleotide… (More)

We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism… (More)

- Vadim N. Biktashev, Mikhail A Tsyganov
- Physical review. E, Statistical, nonlinear, and…
- 2009

We identify a type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis… (More)

- Elena Nikonova, Mikhail A Tsyganov, Walter Kolch, Dirk Fey, Boris N. Kholodenko
- Molecular bioSystems
- 2013

A network of the Rho family GTPases, which cycle between inactive GDP-bound and active GTP-bound states, controls key cellular processes, including proliferation and migration. Activating and… (More)

- Mikhail A Tsyganov, Vadim N. Biktashev
- Physical review. E, Statistical, nonlinear, and…
- 2004

In this paper, we use numerical simulations to demonstrate a half-soliton interaction of waves in a mathematical model of a "prey-predator" system with taxis when of two colliding waves, one… (More)

- Mikhail A Tsyganov, Vadim N. Biktashev
- Physical review. E, Statistical, nonlinear, and…
- 2014

We consider principal properties of various wave regimes in two selected excitable systems with linear cross diffusion in one spatial dimension observed at different parameter values. This includes… (More)