Academic Staff:
Research Student:
Overview:
Ana Sendova-Franks' main research interest is the understanding of social insect colonies, and ants in particular, as models of decentralised adaptive complex organisation honed by natural selection over millions of years. This involves mathematical modelling which is often facilitated by initial individual-based computer models seeking to link individual rules of behaviour with patterns and processes at the colony (population) level. Recent work includes models of task switching in the division of labour, building, worker sorting, as well as work on collective learning and brood sorting. See Ana's homepage for more details.
Rob Laister's main interests are in the qualitative solution behaviour in systems of non-local reaction-diffusion equations.
The term `non-local' means that the nonlinearities depend on population levels at previous times (delay) and/or weighted averages
of the spatial distribution of population densities. Such equations arise naturally in models of infectious diseases or where
resources take time to regenerate.
Recent work has looked at the effects of both degenerate diffusion and non-Lipschitz nonlinearities in bistable reaction-diffusion equations (such as those that arise in the Nagumo equation of nerve impulse propagation, cumbustion theory and population genetics). In particular, novel travelling wave solutions (`catch-up' and `splitting' waves) exist where they otherwise would not in the classical Lipschitz case.
Rob is also interested in the qualitative structure of solutions in differential-algebraic equations (DAEs) and their
applications to quasi-linear PDEs. DAEs take the general form dx/dt = f(x,y), 0=g(x,y) and have interesting, novel solutions
due to a lack of uniqueness at special points in the phase space. In particular they provide a new line of attack when seeking
special solutions (e.g. travelling waves) of PDEs (degenerate elliptic and parabolic, quasi-linear hyperbolic). At present we
are pursuing possible implications for nonlinear lattices.Dr Laister's work is in collaboration with Dr R. Beardmore, Imperial College and Dr A.T. Peplow, KTH, Stockholm.Laister and Beardmore have also proved results on the bifurcation structure of solutions in degenerate elliptic equations. In particular they have shown that a countable collection of continua can bifurcate from a single point and that, for a fixed parameter value, these solutions accumulate on the trivial solution, a so-called `sequential bifurcation.'
Current doctoral studies within this group as follows:
Under the supervision of Ana Sendova-Franks, the aim of Tom Richardson's PhD thesis is to contribute to our understanding of the self-regulatory mechanisms of complex biological systems using experimentation on ant colonies and modelling based on individual threshold distributions for task performance in the context of division of labour. His studentship is part of a multidisciplinary project on how self-regulatory systems work involving physicists (Professor Kim Christensen and Dr Elsa Arcaute, Imperial College), social scientists (Dr Angela Espinosa and her PhD student, University of Hull) and roboticists (Dr Torbjorn Dahl and Faruque Sarker, University of Wales at Newport). Tom Richardson is based at the Ant Lab at the University of Bristol and is co-supervised by Professor Nigel Franks.
Tom Richardson is funded through Sendova Frank's recent EPSRC grant "Defying the rules: how self-regulatory social systems work" [Click here for EPSRC external link]
Under the supervision of Rob Laister, the aim of Zahid Shareef's PhD project is to understand the effects of non-locality (e.g. infection delay or transmission at a distance) on the dynamics of deterministic mathematical models of infectious diseases. In particular they seek to understand the influence of system parameters (e.g. infection rate, diffusion rate, incubation time) on the qualitative solution structure of the models (e.g. convergence to spatial patterns, periodic outbreaks, epidemic waves).
Select Publications:
Aleksiev AS, Sendova-Franks AB, Franks NR, "Nest 'moutling' in the ant Temnothorax albipennis", Animal Behaviour 74, (2007), 567-575.
Aleksiev AS, Longdon, B, Christmas MJ, Sendova-Franks AB, Franks NR, "Individual choice of building material for nest construction by worker ants and the collective outcome for their colony", Animal Behaviour 74, (2007), 559-566.
Aleksiev AS, Sendova-Franks AB, Franks NR "The selection of building material for wall construction by ants", Animal Behaviour 73, (2007), 779-788.
Scholes SR, Sendova-Franks AB, Swift ST & Melhuish C 'Ants can sort their brood without a gaseous template', Behavioral Ecology and Sociobiology 59, (2006), 531-540.
Melhuish C, Sendova-Franks AB, Scholes S, Horsfield I, Welsby F, "Ant-inspired sorting by robots: the importance of initial clustering", Journal of The Royal Society Interface 3, (2006), 235-242.
Laister, Peplow and Beardmore, Travelling waves in continuum models of nonlinear lattices: a DAE approach. ICNAAM 2005: International Conference on Numerical Analysis and Applied Mathematics. 331-334.
Laister and Beardmore, Sequential and Continuum Bifurcations in Degenerate Elliptic Equations. Proc. Amer. Math. Soc. 132(1) (2004).
Laister, Peplow and Beardmore, "Finite Time Extinction in Nonlinear Diffusion Equations". Appl. Math. Lett. 17(5) (2004).
Laister, Beardmore and Peplow, Trajectories of a DAE near a Pseudo Equilibrium. Nonlinearity 17(1) (2004).
Scholes S, Wilson M, Sendova-Franks AB, & Melhuish C, "Comparisons in evolution and engineering: the collective intelligence of sorting", Adaptive Behavior, 12, (2004), 147-159
Sendova-Franks, Scholes, Franks and Melhuish, Brood sorting by ants: two phases and differential diffusion. Animal Behaviour. 68 (2004).
Langridge, Franks and Sendova-Franks, Improvement in collective performance with experience in ants. Behavioral Ecology and Sociobiology. 56 (2004).
Wilson, Melhuish, Sendova-Franks and Scholes, Algorithms for building annular structures with minimalist robots inspired by brood sorting in ant colonies. Autonomous Robots, 17, (2004).
Franks, Britton, Sendova-Franks, Denny, Soans, Brown, Cole, Havardi, Griffiths and Ellis, Centrifugal waste disposal and the optimization of ant nest craters. Animal Behaviour, 67, (2004).
Laister and Beardmore, Transversality and Separation of Zeros in Second Order Differential Equations. Proc. Amer. Math. Soc. 131(1) (2003).
Laister and Beardmore, The Flow of a DAE Near a Singular Equilibrium. SIAM J. Matrix Analysis and Applications. 24(1) (2002).
Laister, "Global Asymptotic Behaviour in some Functional Parabolic Equations". Nonlinear Analysis: TMA 50(3) (2002).
Sendova-Franks and Van lent, Random walk models of worker sorting in ant colonies. Journal of Theoretical Biology, 217, (2002).
Sendova-Franks, Franks and Britton, The role of competition in task switching during colony emigration in the ant Leptothorax albipennis. Animal Behaviour, 63, (2002).
Laister, "Instability of Equilibria in some Delay Reaction-diffusion Systems". J. Math. Anal. Appns. 247(2) (2000).
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