The "CrossInteraction" project made significant progress in several fields of science by applying bifurcation theory to nonlinear dynamical models. This novel approach shed light on the mechanisms underlying abrupt changes in complex systems, contributing to both theoretical advancements and practical applications.
In population biology, the project investigated how climate change-induced seasonal fluctuations influence the threshold and variability of the Allee effect. These changes were shown to destabilize seasonally synchronized ecosystems, leading to cycles of extinction, chaotic dynamics, and hyper-chaotic attractors near the trivial equilibrium, representing population collapse. This instability can remain hidden for extended periods, with sudden transitions triggered by external perturbations, offering critical insights into ecosystem fragility in fragmented landscapes. Moreover, the research demonstrated how cross-feeding interactions can lead to ecosystem asymmetry and branching, culminating in the dominance of a single cross-feeding chain. These findings challenge traditional models and emphasize the multistability of ecosystems, contributing to population and evolutionary biology.
In neuroscience, the project explored neural synchronization mechanisms, essential for motor control, learning, and perception, as well as disorders like epilepsy. By applying bifurcation theory and tools such as Arnold tongues and continuation methods, the research provided a unified framework for studying synchronization scenarios in neuronal networks. Key findings included the identification of phase-shift synchronization patterns, which may correlate with very high-frequency oscillations (VHFOs) observed near epileptic foci. This work advances our understanding of pathological brain activity and introduces a promising approach to identifying new biomarkers for epilepsy, with potential clinical applications.
In epidemiology, the project examined the synchronization of epidemic cycles with seasonal transmission rates, integrating factors like vaccination, immunity, and healthcare capacity. The bifurcation analysis revealed regions of seasonal synchronization that help explain the timing and intensity of outbreaks, including chaotic and quasiperiodic regimes. Chaotic regimes, while unpredictable in detail, were shown to result in more regular winter outbreaks, whereas quasiperiodic dynamics allowed outbreaks to occur at any time of the year. These findings provide valuable insights into managing diseases like COVID-19 and align with historical data on pertussis outbreaks. The research also identified bistability regions, where abrupt shifts in disease prevalence can be triggered by superspreading events or migration, highlighting the role of external factors in epidemic control.
The project's theoretical contributions included the development of bifurcation analysis tools and frameworks for studying nonlinear systems, making complex mathematical concepts accessible and applicable across diverse domains. These tools enabled more accurate predictions of ecosystem stability, neural dynamics, and epidemic cycles, supporting better decision-making in ecology, medicine, and public policy.
The findings were disseminated through peer-reviewed publications and consultations with international experts, ensuring broad scientific impact. The "CrossInteraction" project demonstrated the power of nonlinear dynamics to address challenges across disciplines, from biodiversity conservation to neurological health and epidemic control, delivering insights with both academic and societal relevance.
