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In our lab, we focus on the mathematical modeling and analysis of nonlinear dynamics and complex systems. Our research explores how interactions among individual units—whether neurons, oscillators, or biological agents—give rise to sophisticated collective behaviors. Here is a brief overview of the core research areas we pursue:
In our lab, we focus on the mathematical modeling and analysis of nonlinear dynamics and complex systems. Our research explores how interactions among individual units—whether neurons, oscillators, or biological agents—give rise to sophisticated collective behaviors. Here is a brief overview of the core research areas we pursue:
Chimera States: A major part of our work involves studying chimera states, a fascinating phenomenon in which a network of identical oscillators spontaneously splits into two groups: one that is synchronized and coherent, and another that is desynchronized and incoherent. We investigate how these states emerge in diverse topologies and develop methods to control or induce them within neuronal networks.
Chimera States: A major part of our work involves studying chimera states, a fascinating phenomenon in which a network of identical oscillators spontaneously splits into two groups: one that is synchronized and coherent, and another that is desynchronized and incoherent. We investigate how these states emerge in diverse topologies and develop methods to control or induce them within neuronal networks.
Complex and Higher-Order Networks: We look beyond simple pairwise connections to investigate higher-order interactions. By studying simplicial complexes and hypergraphs, we aim to understand how group-level interactions affect the stability and evolution of a system. We also analyze time-varying networks, in which the connection structure evolves over time.
Complex and Higher-Order Networks: We look beyond simple pairwise connections to investigate higher-order interactions. By studying simplicial complexes and hypergraphs, we aim to understand how group-level interactions affect the stability and evolution of a system. We also analyze time-varying networks, in which the connection structure evolves over time.
Synchronization Phenomena: We explore the fundamental principles of synchronization, examining the mechanisms that allow coupled systems to align their rhythms. Our lab studies various forms of this behavior—including lag, projective, and cluster synchronization—to determine the exact conditions and coupling strengths required for systems to reach a stable state.
Synchronization Phenomena: We explore the fundamental principles of synchronization, examining the mechanisms that allow coupled systems to align their rhythms. Our lab studies various forms of this behavior—including lag, projective, and cluster synchronization—to determine the exact conditions and coupling strengths required for systems to reach a stable state.
Extreme Events: We investigate the mathematical triggers of extreme events—rare, high-magnitude fluctuations in dynamical systems. Our goal is to identify the "precursors" to these events to improve predictability in systems prone to sudden crises, such as power grid failures, cardiac arrhythmias, or ecological collapses.
Extreme Events: We investigate the mathematical triggers of extreme events—rare, high-magnitude fluctuations in dynamical systems. Our goal is to identify the "precursors" to these events to improve predictability in systems prone to sudden crises, such as power grid failures, cardiac arrhythmias, or ecological collapses.
Swarmalators: Our lab is actively studying swarmalators, entities that both "swarm" (move through space) and "oscillate" (change their internal state). We examine how feedback between spatial movement and phase synchronization gives rise to unique collective patterns, such as active phase waves or static clusters.
Swarmalators: Our lab is actively studying swarmalators, entities that both "swarm" (move through space) and "oscillate" (change their internal state). We examine how feedback between spatial movement and phase synchronization gives rise to unique collective patterns, such as active phase waves or static clusters.
Mathematical Biology and Epidemiology: We apply nonlinear mathematical tools to pressing biological challenges, including modeling cancer growth and analyzing how time delays affect treatment outcomes. Additionally, we work on epidemiological modeling, using compartmental structures to predict the spread of infectious diseases like COVID-19 and evaluate the effectiveness of public health interventions.
Mathematical Biology and Epidemiology: We apply nonlinear mathematical tools to pressing biological challenges, including modeling cancer growth and analyzing how time delays affect treatment outcomes. Additionally, we work on epidemiological modeling, using compartmental structures to predict the spread of infectious diseases like COVID-19 and evaluate the effectiveness of public health interventions.
Delay Synchronization and Multiplexing: We explore delay synchronization, in which two layers of oscillators synchronize via an intermediate "delay" layer without a direct connection. We typically study this within the framework of multilayer and multiplex networks, which offer more realistic representations of complex, layered infrastructures.
Delay Synchronization and Multiplexing: We explore delay synchronization, in which two layers of oscillators synchronize via an intermediate "delay" layer without a direct connection. We typically study this within the framework of multilayer and multiplex networks, which offer more realistic representations of complex, layered infrastructures.
Chaos Control and Secure Communication: Finally, we study chaotic systems and methods to control them. By synchronizing chaotic transmitters and receivers, we develop frameworks for secure communication that mask sensitive information within chaotic signals and allow it to be decrypted by a synchronized partner system.
Chaos Control and Secure Communication: Finally, we study chaotic systems and methods to control them. By synchronizing chaotic transmitters and receivers, we develop frameworks for secure communication that mask sensitive information within chaotic signals and allow it to be decrypted by a synchronized partner system.
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