Related papers: A two-dimensional swarmalator model with higher-or…
Synchronization of coupled oscillators is observed in many natural and engineered systems and emerges due to the interactions within the system. It can be both beneficial, e.g., in power grids, and harmful, e.g., in epileptic seizures. In…
Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson…
We study a system of globally coupled FitzHugh-Nagumo oscillators, showing that the presence of higher-order interactions affects the character of the transition between synchronous and asynchronous states. In particular, we demonstrate…
We study the effects of phase-frustrated, higher-order interactions in a system of coupled phase oscillators with two communities. We use dimensionality reduction techniques to derive a low-dimensional system of ODEs to describe the…
We present some recent development in modeling concurrent emergence of collective behaviors, namely, the emergence of clustering, flocking and synchronization at the same time. We derive two new models, namely Swarmalator-Vicsek and…
The high-dimensional generalization of the one-dimensional Kuramoto paradigm has been an essential step in bringing about a more faithful depiction of the dynamics of real-world systems. Despite the multi-dimensional nature of the…
How higher-order interactions influence dynamical behavior in networks of coupled chaotic oscillators remains an open question. To address this, we investigate emergent dynamical behaviors in a wheel network of R\"ossler and Lorenz…
We investigate a new class of topological travelling-wave solutions for a macroscopipc swarmalator model involving force non-reciprocity. Swarmalators are systems of self-propelled particles endowed with a phase variable. The particles are…
Time delay can have a significant impact on the properties of collective organization of active matter. In the previous paper [1], we discussed delay-induced breathing in a system of swarmalators - a model coupling particles' internal…
We study a population of swarmalators (swarming/mobile oscillators) which run on a ring and are subject to random pinning. The pinning represents the tendency of particles to stick to defects in the underlying medium which competes with the…
We show that a two-dimensional system of flocking microswimmers interacting hydrodynamically can be expressed using a Hamiltonian formalism. The Hamiltonian depends strictly on the angles between the particles and their swimming…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make…
We explore a simplified class of models we call swarms, which are inspired by the collective behavior of social insects. We perform a mean-field stability analysis and perform numerical simulations of the model. Several interesting types of…
Recent studies have investigated various dynamic processes characterizing collective behaviors in real-world systems. However, these dynamics have been studied individually in specific contexts. In this article, we present a holistic…
Group behavior has received much attention as a test case of self-organization. There has been much written in recent years to investigate interactions within groups of agents. These agents can be animals moving in an interactive way, such…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
Higher-order interactions that nonlinearly couple more than two nodes are important in many networked systems, and their effects on collective dynamics are increasingly being studied. Here we provide an overview of this rapidly growing…
We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…
Chimera states are synchronization patterns in which coherent and incoherent regions coexist in systems of identical oscillators. This elusive phenomenon has attracted significant interest and has been widely analyzed, revealing several…