Nonlinear dynamics and evolution
Research at The NoDE Lab (web)
Our laboratory seeks to understand nonlinear phenomena. Our research is focused on different biological systems, from prebiotic replicators to complex ecosystems and disease dynamics. To do so we use the qualitative theory of dynamical systems and computer simulations (stochastic dynamics and spatially-extended 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 or tumor cells extinctions. Also, we are doing research in general topics of nonlinear dynamical systems such as bifurcations, universality phenomena, scaling, and transients.
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Keywords of our research lines
- - Dynamical systems - Differential equations; Bifurcations, Chaos; Maps.
- - Mathematical medicine - Virology; Immunology; Cancer; Disease-free attractors
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- .Cancer dynamical systems - Cancer heterogeneity; Cancer-free attractors; Tumor evolution; Genomic instability thresholds; Modelling of targeted cancer therapies.
- .Dynamics and evolution of RNA virus - Quasispecies theory; Error catastrophe; Lethal mutagenesis; Multipartite virus; Viral evolution.
- - Theoretical ecology and systems Biology - Arid and semiarid ecosystems; Tipping points and catastrophes; Warning signals in ecosystems; Predator-prey dynamicsGene circuits; Bistability; Multistability; Cell fate decision.
- - Origins of life - Prebiotic evolution; Quasispecies; Hypercycles; Increase of information