Secret History: Return of the Black Death Channel 4, 7-8pm In 1348 the Black Death swept through London, killing people within days of the appearance of their first symptoms. Exactly how many died, and why, has long been a mystery. This Secret History documentary follows experts as they pick through the evidence and reveal why the plague killed on such a scale. And they ask, what might be coming next?

Medscape

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

From the Publisher:
This book is for people who need to solve ordinary differential equations (ODEs), both initial value problems (IVPs) and boundary value problems (BVPs) as well as delay differential equations (DDEs). These topics are usually taught in separate courses of length one semester each, but solving ODEs with Matlab provides a sound treatment of all three in about 250 pages. The chapters on each of these topics begin with a discussion of "the facts of life" for the problem, mainly by means of examples. Numerical methods for the problem are then developed - but only the methods most widely used. Although the treatment of each method is brief and technical issues are minimized, the issues important in practice and for understanding the codes are discussed. Often solving a real problem is much more than just learning how to call a code. The last part of each chapter is a tutorial that shows how to solve problems by means of small but realistic examples.

/pdf/solving-odes-with-matlab-1yxxtyf9zz.pdf

Solving ODEs with MATLAB

The theory of asymptotic speeds of spread and monotone traveling waves is established for a class of monotone discrete and continuous-time semiflows and is applied to a functional differential equation with diffusion, a time-delayed lattice population model and a reaction-diffusion equation in an infinite cylinder. c � 2006 Wiley Periodicals, Inc.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/cpa.20221

Asymptotic speeds of spread and traveling waves for monotone semiflows with applications

This paper deals with the existence of traveling wave front solutions of reaction-diffusion systems with delay. A monotone iteration scheme is established for the corresponding wave system. If the reaction term satisfies the so-called quasimonotonicity condition, it is shown that the iteration converges to a solution of the wave system, provided that the initial function for the iteration is chosen to be an upper solution and is from the profile set. For systems with certain nonquasimonotone reaction terms, a convergence result is also obtained by further restricting the initial functions of the iteration and using a non-standard ordering of the profile set. Applications are made to the delayed Fishery–KPP equation with a nonmonotone delayed reaction term and to the delayed system of the Belousov–Zhabotinskii reaction model.

/pdf/traveling-wave-fronts-of-reaction-diffusion-systems-with-2zfggrx2b7.pdf

Traveling Wave Fronts of Reaction-Diffusion Systems with Delay

Two different approaches are employed to investigate the global attractivity of delayed Hopfield neural network models. Without assuming the monotonicity and differentiability of the activation functions, Liapunov functionals and functions (combined with the Razumikhin technique) are constructed and employed to establish sufficient conditions for global asymptotic stability independent of the delays. In the case of monotone and smooth activation functions, the theory of monotone dynamical systems is applied to obtain criteria for global attractivity of the delayed model. Such criteria depend on the magnitude of delays and show that self-inhibitory connections can contribute to the global convergence.

Global attractivity in delayed Hopfield neural network models

In this paper, we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment. We show that if the mature deat...

A reaction–diffusion model for a single species with age structure. I Travelling wavefronts on unbounded domains

A recent field manipulation on a terrestrial vertebrate showed that the fear of predators alone altered anti-predator defences to such an extent that it greatly reduced the reproduction of prey. Because fear can evidently affect the populations of terrestrial vertebrates, we proposed a predator-prey model incorporating the cost of fear into prey reproduction. Our mathematical analyses show that high levels of fear (or equivalently strong anti-predator responses) can stabilize the predator-prey system by excluding the existence of periodic solutions. However, relatively low levels of fear can induce multiple limit cycles via subcritical Hopf bifurcations, leading to a bi-stability phenomenon. Compared to classic predator-prey models which ignore the cost of fear where Hopf bifurcations are typically supercritical, Hopf bifurcations in our model can be both supercritical and subcritical by choosing different sets of parameters. We conducted numerical simulations to explore the relationships between fear effects and other biologically related parameters (e.g. birth/death rate of adult prey), which further demonstrate the impact that fear can have in predator-prey interactions. For example, we found that under the conditions of a Hopf bifurcation, an increase in the level of fear may alter the direction of Hopf bifurcation from supercritical to subcritical when the birth rate of prey increases accordingly. Our simulations also show that the prey is less sensitive in perceiving predation risk with increasing birth rate of prey or increasing death rate of predators, but demonstrate that animals will mount stronger anti-predator defences as the attack rate of predators increases.

Xingfu Zou

Papers

Traveling Wave Fronts of Reaction-Diffusion Systems with Delay

Global attractivity in delayed Hopfield neural network models

A reaction–diffusion model for a single species with age structure. I Travelling wavefronts on unbounded domains

Modelling the fear effect in predator–prey interactions

Exponential stability of Cohen-Grossberg neural networks