Periodic Reporting for period 1 - CrossInteractions (Models with cross interactions between partial dynamical processes aiming to understand significant or abrupt dynamic changes.)
Reporting period: 2022-12-01 to 2024-11-30
The purpose of the "CrossInteractions" project is to study and understand crucial events in nonlinear dynamical systems, with a special emphasis on bifurcations that often signal abrupt and significant shifts in system behavior. By modeling such transitions, the research aims to enhance predictive capabilities, inform state-of-the-art strategies, and establish best practices in fields such as population biology, neurology, and epidemiology.
The motivation for this study stems from the urgent need to decipher and control complex systems where small changes can lead to significant effects on behavior. Such transitions are frequently observed in ecosystems affected by disturbances, neural networks governing brain activity, and the spread of infectious diseases. This study seeks to explain these shifts using bifurcation theory, thereby providing both theoretical frameworks and practical decision-making tools.
In population biology, the study examines the dynamic interplay of prey-predator systems in fragmented habitats, focusing on how interagent interactions affect the stability, persistence, and biodiversity of species within ecosystems. Understanding chaotic and periodic patterns in these systems is crucial for conservation and ecosystem management.
The neurological component of the study analyzes how modular neuronal subsystems influence synchronization dynamics and conflicts in neural activity. These transitions often arise from synchronization events, which play a critical role in motor control, learning, and perception. Using bifurcation theory, the research investigates the mechanics underlying transient behaviors, particularly their implications for disorders such as focal epilepsy. This includes studying high-frequency oscillations (HFOs) and phase synchronization in interconnected neuronal networks, offering insights into novel biomarkers for epilepsy and other synchronization-related neurological disorders. The findings aim to advance neuroscience and provide new approaches to managing neurological diseases, ultimately improving clinical outcomes.
The epidemiological aspect of the project focuses on how seasonal variations, vaccination strategies, and other external factors influence the progression of infectious disease epidemics. The results will directly inform public health decision-making, enhancing preparedness and mitigation strategies for future outbreaks. By exploring the interaction between epidemic cycles and seasonality, this research provides actionable insights into managing diseases such as COVID-19.
The "CrossInteractions" project bridges mathematical biology, social sciences, and public health to ensure both social relevance and theoretical rigor. By promoting multidisciplinary collaboration and making mathematical tools accessible, the project highlights their applicability in real-world scenarios. Its emphasis on open research, sustainability, and international cooperation underscores the goal of maximizing societal impact.
The expected outputs of "CrossInteractions" include the development of theoretical knowledge, predictive models, and sustainable solutions for environmental policy, healthcare, and public policy. These contributions are anticipated to have a far-reaching impact, aiding in biodiversity conservation, improving neurological health, and guiding epidemic control strategies. By addressing fundamental socioeconomic and ecological challenges, the project is both academically significant and practically relevant.
The motivation for this study stems from the urgent need to decipher and control complex systems where small changes can lead to significant effects on behavior. Such transitions are frequently observed in ecosystems affected by disturbances, neural networks governing brain activity, and the spread of infectious diseases. This study seeks to explain these shifts using bifurcation theory, thereby providing both theoretical frameworks and practical decision-making tools.
In population biology, the study examines the dynamic interplay of prey-predator systems in fragmented habitats, focusing on how interagent interactions affect the stability, persistence, and biodiversity of species within ecosystems. Understanding chaotic and periodic patterns in these systems is crucial for conservation and ecosystem management.
The neurological component of the study analyzes how modular neuronal subsystems influence synchronization dynamics and conflicts in neural activity. These transitions often arise from synchronization events, which play a critical role in motor control, learning, and perception. Using bifurcation theory, the research investigates the mechanics underlying transient behaviors, particularly their implications for disorders such as focal epilepsy. This includes studying high-frequency oscillations (HFOs) and phase synchronization in interconnected neuronal networks, offering insights into novel biomarkers for epilepsy and other synchronization-related neurological disorders. The findings aim to advance neuroscience and provide new approaches to managing neurological diseases, ultimately improving clinical outcomes.
The epidemiological aspect of the project focuses on how seasonal variations, vaccination strategies, and other external factors influence the progression of infectious disease epidemics. The results will directly inform public health decision-making, enhancing preparedness and mitigation strategies for future outbreaks. By exploring the interaction between epidemic cycles and seasonality, this research provides actionable insights into managing diseases such as COVID-19.
The "CrossInteractions" project bridges mathematical biology, social sciences, and public health to ensure both social relevance and theoretical rigor. By promoting multidisciplinary collaboration and making mathematical tools accessible, the project highlights their applicability in real-world scenarios. Its emphasis on open research, sustainability, and international cooperation underscores the goal of maximizing societal impact.
The expected outputs of "CrossInteractions" include the development of theoretical knowledge, predictive models, and sustainable solutions for environmental policy, healthcare, and public policy. These contributions are anticipated to have a far-reaching impact, aiding in biodiversity conservation, improving neurological health, and guiding epidemic control strategies. By addressing fundamental socioeconomic and ecological challenges, the project is both academically significant and practically relevant.
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.
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.
The "CrossInteractions" project has delivered significant results beyond the current state of the art in population biology, neuroscience, and epidemiology, with potential impacts spanning academic, societal, and policy-making domains.
Key Results and Potential Impacts:
Population Biology: The project introduced novel mathematical frameworks to analyze prey-predator interactions across fragmented habitats. These models revealed how spatial interactions and cross-patch dynamics influence ecosystem stability, persistence, and biodiversity. By identifying mechanisms of chaotic and periodic patterns, the research contributes to improving ecosystem management strategies. These insights can inform conservation policies and enhance environmental planning frameworks.
Neuroscience: The application of bifurcation theory to neuronal networks provided new insights into epileptic biomarkers and phase-shifted synchronization phenomena. These findings have implications for understanding neural disorders such as epilepsy, potentially leading to the development of new diagnostic and therapeutic tools. Further interdisciplinary collaboration and funding could facilitate the clinical validation of these results and their integration into neuroscience research and practice.
Epidemiology: The project’s models incorporating seasonality, vaccination dynamics, and immunity have advanced predictions of infectious disease transmission and control strategies. By improving the understanding of epidemic waves and their synchronization with season, the project contributes to better public health preparedness and pandemic management policies. These results can be further developed into decision-support tools for epidemiological modeling and integrated into public health systems.
To ensure the broader uptake and success of these results, the following steps are recommended:
Further Research: Focus on cross-interactions in population biology, incorporating added seasonality to enhance ecological models. In epidemiology, investigate cross-interactions between variants and regions to better understand the dynamics of disease spread.
Interdisciplinary Collaboration: Foster stronger ties between mathematicians, biologists, neuroscientists, and public health experts to expand the scope of applications.
Funding and Commercialization: Seek additional funding for clinical validation of neuroscience findings
Internationalization: Leverage international collaborations to disseminate methods and findings across global networks, fostering widespread adoption.
Key Results and Potential Impacts:
Population Biology: The project introduced novel mathematical frameworks to analyze prey-predator interactions across fragmented habitats. These models revealed how spatial interactions and cross-patch dynamics influence ecosystem stability, persistence, and biodiversity. By identifying mechanisms of chaotic and periodic patterns, the research contributes to improving ecosystem management strategies. These insights can inform conservation policies and enhance environmental planning frameworks.
Neuroscience: The application of bifurcation theory to neuronal networks provided new insights into epileptic biomarkers and phase-shifted synchronization phenomena. These findings have implications for understanding neural disorders such as epilepsy, potentially leading to the development of new diagnostic and therapeutic tools. Further interdisciplinary collaboration and funding could facilitate the clinical validation of these results and their integration into neuroscience research and practice.
Epidemiology: The project’s models incorporating seasonality, vaccination dynamics, and immunity have advanced predictions of infectious disease transmission and control strategies. By improving the understanding of epidemic waves and their synchronization with season, the project contributes to better public health preparedness and pandemic management policies. These results can be further developed into decision-support tools for epidemiological modeling and integrated into public health systems.
To ensure the broader uptake and success of these results, the following steps are recommended:
Further Research: Focus on cross-interactions in population biology, incorporating added seasonality to enhance ecological models. In epidemiology, investigate cross-interactions between variants and regions to better understand the dynamics of disease spread.
Interdisciplinary Collaboration: Foster stronger ties between mathematicians, biologists, neuroscientists, and public health experts to expand the scope of applications.
Funding and Commercialization: Seek additional funding for clinical validation of neuroscience findings
Internationalization: Leverage international collaborations to disseminate methods and findings across global networks, fostering widespread adoption.