Overview
Qualifications
1- Ph.D, Applied Mathematics (University of Exeter, UK, October 2013)
2- M.Sc in Mathematics (University of Benghazi, Libya, August 2003)
3- B.Sc in Mathematics, Statistics and Education (University of Benghazi, Libya, January 1999)
Publications
Key publications | Publications by category | Publications by year
Key publications
Elragig A, Townley S (2012). A new necessary condition for Turing instabilities.
Math Biosci,
239(1), 131-138.
Abstract:
A new necessary condition for Turing instabilities.
Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community.
Abstract.
Author URL.
Publications by category
Journal articles
Elragig A, Townley S (2012). A new necessary condition for Turing instabilities.
Math Biosci,
239(1), 131-138.
Abstract:
A new necessary condition for Turing instabilities.
Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community.
Abstract.
Author URL.
Publications by year
2012
Elragig A, Townley S (2012). A new necessary condition for Turing instabilities.
Math Biosci,
239(1), 131-138.
Abstract:
A new necessary condition for Turing instabilities.
Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community.
Abstract.
Author URL.
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