Systems Biology and nonlinearity

Theoretical ecology: Functional shifts in species; semiarid ecosystems; tipping points (bifurcations); biodiversity loss; warning signals.

Dynamics and evolution of RNA viruses: Quasispecies theory; Defective interfering particles; Multipartite virus; Viral evolution.

Cancer dynamics and evolution: Cancer heterogeneity and phenotypic quasispecies; Cancer-free attractors; Tumour evolution and genomic instability; Modelling targeted cancer therapies; Tumour immunogenicity; Epigenetic regulation. 

Image below: multiscroll attractor visualised in an oscilloscope

Research on nonlinear dynamics and evolution

Our research seeks to understand nonlinear phenomena focusing on biological processes at different scales, from prebiotic replicators to complex ecosystems and disease dynamics.  To do so we use the qualitative theory of dynamical systems. We investigate the dynamical evolution of nonlinear systems, paying special attention to the bifurcations and phase transitions separating relevant dynamical phenomena. Our investigations have the ultimate goal to identify potential useful dynamical scenarios such as ecosystems recovery, virus clearance, and tumor cells' extinction. Basic research on these topics can have a big impact in the Ecological and Biomedical sciences.

Image below: multi scroll attractor from electronic circuit equations