Related papers: Ensemble order parameter equations in star network
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
The continuous phase transition, indicated by the macroscopic order parameter and the occurrence of the spontaneous symmetry breaking, is well illustrated based on the Ginzburg-Landau's paradigm. In systems described by one order parameter,…
Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the brain, where a large repertoire of different dynamics,…
The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on $N$-torus defined as coupled harmonic oscillators. The order parameter is often used to measure the degree of synchronization.…
In this work, a novel approach for the reliable and efficient numerical integration of the Kuramoto model on graphs is studied. For this purpose, the notion of order parameters is revisited for the classical Kuramoto model describing…
Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of…
We study the effect of network topology on the collective dynamics of an oscillator ensemble. Specifically, we explore explosive synchronization in a system of interacting star networks. Explosive synchronization is characterized by an…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
The equilibrium properties of allocation algorithms for networks with a large number of nodes with finite capacity are investigated. Every node is receiving a flow of requests and when a request arrives at a saturated node, i.e. a node…
Within the framework of an exactly solvable model, which takes into account the interaction of fluctuating modes with equal and opposite momenta, we consider phase diagrams in systems with coupled scalar order parameters. We show that, in…
We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is…
We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, that gives full an- alytical description of states, rotating with constant frequency. For…
We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant…
Phase balanced states are a highly under-explored class of solutions of the Kuramoto model and other coupled oscillator models on networks. So far, coupled oscillator research focused on phase synchronized solutions. Yet, global constraints…
The multidimensional Kuramoto model describes the synchronization dynamics of particles moving on the surface of D-dimensional spheres, generalizing the original model where particles were characterized by a single phase. In this setup,…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
We show that in small and low density systems described by a lattice gas model with fixed number of particles the location of a thermodynamic phase transition can be detected by means of the distribution of the fluctuations related to an…
We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the…
The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and…
Collective synchronization is often summarized by a complex order parameter $R e^{i\Psi}$, implicitly treating the global phase $\Psi$ as a meaningful macroscopic coordinate. Here we ask when $\Psi$ becomes \emph{operationally well-defined}…