• Theoretical Ecology 

Dynamics in ecosystems arise from different ecological interactions: competition, cooperation, or antagonistic dynamics. Such nonlinear feedbacks are responsible for non-trivial dynamics and tipping points (bifurcations). On top of the deterministic skeleton driven by such ecological interactions, other features such as intrinsic noise and the inherent heterogeneity in species play an important role in the fate of ecosystems' dynamics. In this research line, we are analyzing dynamical models to understand the mechanisms driving ecosystems and diversity to collapse, focusing on the role of demographic fluctuations and spatial dynamics. The identification of such tipping points becomes crucial to determine the nature of transitions and the associated transients.

Interests:  population dynamics; biodiversity preservation; ecosystem services; functional shifts in species; Marine Protected Areas (MPAs); transients; tipping points (bifurcations); warning signals.

• Virus evolutionary dynamics 

RNA viruses are obligate pathogens infecting all types of organisms. They are characterised by fast replication rates and large mutation rates. The interplay between these two processes gives place to extremely interesting dynamical and evolutionary phenomena with deep implications in pathogenesis, virulence, and infectiousness. Within this field, quasispecies theory plays an important role in modelling the evolutionary dynamics of RNA viruses. We are doing research on plant an animal viruses, being interested on the interplay between full-length virus and subviral particles such as defective interfering particles and satellites. We are also interested in stochasticity and co-evolutionary traits between viruses-hosts and immune system interactions. We especially focus on bifurcation theory and in potential scenarios of virus clearance for several important diseases such as hepatitis or human immunodeficiency virus type-1. 

Interests:  virus dynamics and evolution; defective/therapeutic interfering particles; quasispecies theory and virus diversity; dynamics on sequence space

• Mathematical oncology

Cancer is a genetic disease involving an uncontrolled proliferation of cells that ultimately can drive to metastasis. Cancer and tumour dynamics is amongst the most complex biological processes since it involves an entangled array of ecological and evolutionary multi-scale phenomena. We are interested in the understanding of cancer behaviour in order to identify potential scenarios for tumour extinction in terms of bifurcation theory. Especially importance is given to the interplay of cancer cells population dynamics and tumour microevolution, focusing our research on both genotypic and phenotypic traits in cancer. We are also investigating dynamics of oncolytic viruses and immunotherapy as novel and effective future ways to treat cancer and unveil mechanisms behind tumour fragility or clearance.

Interests:  tumor heterogeneity; cancer immunogenicity; mathematical immunotherapy; cancer epigenetics; targeted cancer therapies; oncolytic viruses.

• Nonlinear physiology and brain dynamics

This research line explores nonlinear brain dynamics and physiological conditions in mountaineers and extreme sports athletes by applying tools from dynamical systems theory and advanced time series analyses. By investigating how neural activity adapts under conditions of physical and environmental extremes, we aim to uncover fundamental principles of brain function and resilience. This research bridges neuroscience, applied mathematics, and high-performance physiology, offering insights into cognitive stability and adaptability in challenging, real-world contexts. One of the main goals is to relate dynamical processes with risk management and decision-making in mountain environments, working in close collaboration with mountain guides and runners.

Interests: brain dynamics; EEGs, mountaineering; physiological responses; nonlinearity; attractors; time series analysis; entropy; multifractal analysis.