Research Highlights
Higher-order interaction induced chimeralike state in a bipartite network
We report higher-order coupling induced stable chimeralike state in a bipartite network of coupled phase oscillators without any time-delay in the coupling. We show that the higher-order interaction breaks the symmetry of the homogeneous synchronized state to facilitate the manifestation of symmetry breaking chimeralike state. In particular, such symmetry breaking manifests only when the pairwise interaction is attractive and higher-order interaction is repulsive, and vice versa. Further, we also demonstrate the increased degree of heterogeneity promotes homogeneous symmetric states in the phase diagram by suppressing the asymmetric chimeralike state. We deduce the low-dimensional evolution equations for the macroscopic order parameters using Ott-Antonsen ansatz and obtain the bifurcation curves from them using the software xppaut, which agrees very well with the simulation results. We also deduce the analytical stability conditions for the incoherent state, in-phase and out-of-phase synchronized states, which match with the bifurcation curves.
Disparity-driven heterogeneous nucleation in finite-size adaptive networks
Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single step and multistep phase transitions to global synchronization in a finite-size adaptive network due to the trade off between time scale adaptation and coupling strength disparities. Specifically, small intracluster nucleations coalesce either at the population interface or within the populations resulting in the two distinct phase transitions depending on the degree of the disparities. We find that the coupling strength disparity largely controls the nature of phase transition in the phase diagram irrespective of the adaptation disparity. We provide a mesoscopic description for the cluster dynamics using the collective coordinates approach that brilliantly captures the multicluster dynamics among the populations leading to distinct phase transitions. Further, we also deduce the upper bound for the coupling strength for the existence of two intraclusters explicitly in terms of adaptation and coupling strength disparities. These insights may have implications across domains ranging from neurological disorders to segregation dynamics in social networks.
Exotic Swarming dynamics of High-Dimensional Swarmalators
Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. Swarmalator models employed so far in the literature comprise only one-dimensional phase variables to represent the intrinsic dynamics of the natural collectives. Nevertheless, the latter can indeed be represented more realistically by high-dimensional phase variables. For instance, the alignment of velocity vectors in a school of fish or a flock of birds can be more realistically set up in three-dimensional space, while the alignment of opinion formation in population dynamics could be multidimensional, in general. We present a generalized 𝐷-dimensional swarmalator model, which more accurately captures self-organizing behaviors of a plethora of real-world collectives by self-adaptation of high-dimensional spatial and phase variables. For a more sensible visualization and interpretation of the results, we restrict our simulations to three-dimensional spatial and phase variables. Our model provides a framework for modeling complicated processes such as flocking, schooling of fish, cell sorting during embryonic development, residential segregation, and opinion dynamics in social groups. We demonstrate its versatility by capturing the maneuvers of a school of fish, qualitatively and quantitatively, by a suitable extension of the original model to incorporate appropriate features besides a gallery of its intrinsic self-organizations for various interactions. We expect the proposed high-dimensional swarmalator model to be potentially useful in describing swarming systems and programmable and reconfigurable collectives in a wide range of disciplines, including the physics of active matter, developmental biology, sociology, and engineering.
Effect of higher-order interactions on chimera states in two populations of Kuramoto oscillators
We investigate the effect of the fraction of pairwise and higher-order interactions on the emergent dynamics of the two populations of globally coupled Kuramoto oscillators with phase-lag parameters. We find that the stable chimera exists between saddle-node and Hopf bifurcations, while the breathing chimera lives between Hopf and homoclinic bifurcations in the two-parameter phase diagrams.We investigate the effect of the fraction of pairwise and higher-order interactions on the emergent dynamics of the two populations of globally coupled Kuramoto oscillators with phase-lag parameters. We find that the stable chimera exists between saddle-node and Hopf bifurcations, while the breathing chimera lives between Hopf and homoclinic bifurcations in the two-parameter phase diagrams.
Our Interest Areas
Cascading Failure and Mitigation in Complex Networks
In the intricate fabric of complex networks, the phenomenon of cascading failure looms as a critical challenge. Cascading failure occurs when the failure of a single component within the network triggers a domino effect, propagating through interconnected nodes and leading to widespread system breakdown. This dynamic process poses significant risks to various systems, from power grids and transportation networks to social media platforms and financial systems. Mitigating cascading failure demands a multifaceted approach, encompassing both proactive measures and reactive strategies. These may include enhancing network resilience through redundancy and robustness, implementing targeted monitoring and early warning systems, and developing adaptive control mechanisms to contain and mitigate the impact of failures. As we delve deeper into understanding the complexities of cascading failure, our quest for effective mitigation strategies remains paramount in ensuring the stability and resilience of interconnected systems.
Synchronization Phenomena
Synchronization, a fundamental concept across various domains, entails the coordination of multiple elements to operate in harmony or alignment. From intricate biological processes to complex technological systems, synchronization plays a pivotal role in facilitating coherent and efficient operation. In communication systems, synchronization ensures accurate signal transmission and reception, while in distributed computing, it coordinates concurrent processes to maintain data integrity. Biological systems rely on synchronization for regulating essential functions like neuronal firing and circadian rhythms. As we delve deeper into understanding synchronization mechanisms, we uncover their critical significance in fostering stability and coherence across diverse systems. This introduction sets the stage for exploring the multifaceted aspects of synchronization and its pervasive influence in both natural and engineered systems.
Ageing Transitions in Phase Oscillators
In networks of coupled oscillators, the aging transition refers to the evolution of collective behavior influenced by the gradual degradation of individual components. This phenomenon is studied using macroscopic order parameters derived under strong coupling conditions, which capture the overall dynamics of the network. The transition highlights how changes in the network’s structure and connectivity, influenced by factors like heterogeneity among oscillators and feedback mechanisms, affect its stability and functionality over time. Critical stability analysis based on these parameters identifies thresholds where the network shifts between different states, offering insights into its resilience and response to internal and external influences as it ages.
Swarming Dynamics
Swarming dynamics describes the collective behavior observed in groups of entities, whether animals, insects, or artificial agents, as they move together in a synchronized manner. Through simple local interactions, individuals within the swarm exhibit emergent behaviors such as flocking or schooling, without the need for centralized control. This phenomenon finds applications across diverse fields, including robotics and biology, where researchers explore swarming algorithms for tasks such as collective transport and navigation. Understanding swarming dynamics involves analyzing how individual interactions give rise to complex collective patterns. By leveraging these principles, researchers strive to design efficient and scalable systems for various applications, from distributed sensing to disaster response and urban planning.
Adaptive Dynamic Networks
An adaptive dynamics network is a dynamic system comprised of interconnected nodes that continuously adapt their connections and behavior in response to changing circumstances. These networks differ from static ones by allowing for the evolution of connections over time, driven by feedback loops, environmental cues, or individual node interactions. By modeling the adaptive behavior of complex systems, such as biological networks or social structures, researchers gain insights into the emergence of patterns, resilience to disruptions, and the optimization of network performance. Adaptive dynamics networks serve as powerful tools for understanding the intricate interplay between structure and function in dynamic systems, guiding strategies for adaptation and intervention in diverse fields.
Population Ecology
Population ecology is a cornerstone of computational biology and theoretical ecology, dealing with the biodiversity and persistence of an ecosystem primarily through the lens of spatio-temporal species population dynamics. Specific essential parameters, particular to the ecosystem in question, govern the population dynamics of an ecosystem and thus majorly influence the extinction risk of ecosystems. Such parameters quantify biotic and abiotic phenomena like the death rate of a species, the birth rate of a species, immigration, emigration, trophic and non-trophic interspecies and intraspecies interactions, as well as eco-environmental interactions, like climate change, habitat loss, and human influence. Factoring in these parameters, the population dynamics of ecosystems are described by prey-predator models, which are essentially nonlinear and can be analyzed using the robust structure of nonlinear dynamics. This fundamentally ‘physical’ approach to theoretical ecology has resulted in several remarkable observations and predictions (e.g., Figure 1. From Blasius and Stone, 1991). Not only do these models exhibit features of traditional nonlinear dynamics like chaoticity, but we can extend them readily to construct complex networks of food -webs ( i.e., multi-species oscillator models), which accurately describe the intricacies of a natural ecosystem. We live in ecosystems, and understanding what keeps them alive is what keeps us alive, and NLD can help us keep it that way.
About logo: The butterfly logo embodies the profound concept that complex and chaotic processes can give rise to astonishing beauty. Much like the intricate wings of a butterfly emerge from chaotic trajectories within a Lorenz attractor, our logo’s design symbolizes this convergence of chaos and creativity. The wings, crafted from the dynamic patterns of the Lorenz attractor, reflect the intricate dance of unpredictability. They are intricately connected to the main body, which represents a complex network, symbolizing the interconnectedness of diverse elements within our field. Together, these elements converge to create something truly beautiful, enriching our understanding of nature’s complexities and inspiring awe in its intricate design.
~ Karan & Akash