Abstract We study a rock–paper–scissors model for competing populations that exhibits travelling waves in one spatial dimension and spiral two dimensions. A characteristic feature of the is presence robust heteroclinic cycle involves three saddle equilibria. The also has fronts are connections between equilibria moving frame reference, but these unstable . However, we find large-wavelength can ...

The intracellular viral life-cycle is an important process in tumor virotherapy. Most mathematical models for tumor virotherapy do not incorporate the intracellular viral life-cycle. In this article, a model for tumor virotherapy with the intracellular viral life-cycle is presented and studied. The period of the intracellular viral life-cycle is modeled as a delay parameter. The model is a nonl...

For dynamical systems possessing invariant subspaces one can have a robust homoclinic cycle to a chaotic set. If such a cycle is stable, it manifests itself as long periods of quiescent chaotic behaviour interrupted by sudden transient 'bursts'. The time between the transients increases as the trajectory approaches the cycle. This behavior for a cycle connecting symmetrically related chaotic se...