We provide an analytic solution of the Rössler equations based on the asymptotic limit $c\to \infty $ and we show in this limit that the solution takes the form of multiple pulses, similar to “burst” firing of neurons. We are able to derive an approximate Poincaré map for the solutions, which compares reasonably with a numerically derived map.

A calculation model is put forward to analyze the interfacial response of an elastic frictionless punch, pressed normally into a half-plane, and subject to bending moment throughout this paper to observe the important effect that different normal loads and bending moments on the contact pressure distribution and contact deformation. Results for the detailed considerations have been given to the specific different cases of ηc. A characteristic response of the punch to a surplus bending moment has been found. The small differences can be observed between both methods show characteristic features of the FEM model and the theoretical model. The presented numerical results illustrate the influences of the normal load and bending moment on the contact stresses. The results obtained can be used to analyze the crack nucleation in fretting when the punch is acted upon by the normal force and the bending moment.

We consider the spread of a general epidemic amongst a population consisting of invididuals with differing susceptibilities to the disease. Deterministic and stochastic versions of the basic model are described and analysed. For both versions of the model we show that assuming a uniform susceptible population, with average susceptibility, leads to an increased spread of infection. We also show how our results can be extended to the carrier-borne epidemic model of Weiss (1965).