Related papers: Dynamics due to competitive flip cycles in active …
The nonequilibrium dynamics of a cycling three-state Potts model is studied on a square lattice using Monte Carlo simulations and continuum theory. This model is relevant to chemical reactions on a catalytic surface and to molecular…
Many types of spatiotemporal patterns have been observed under nonequilibrium conditions. Cycling through four or more states can provide specific dynamics, such as the spatial coexistence of multiple phases. However, transient dynamics…
We studied the nonequilibrium dynamics of a cycling three-state Potts model using simulations and theory. This model can be tuned from thermal-equilibrium to far-from-equilibrium conditions. At low cycling energy, the homogeneous dominant…
We studied the long-term nonequilibrium dynamics of $q$-state Potts models with $q=4$, $5$, $6$, and $8$ using Monte Carlo simulations on a two-dimensional square lattice. When the contact energies between the nearest neighbors for the…
Wave propagation can be observed in various nonequilibrium systems. In this study, we investigated the properties of several wave modes in active six-state Potts models using Monte Carlo simulations of square and hexagonal lattices.…
We study a three-state Potts model extended by allowing cyclic dominance between the states as it appears for the rock-scissors-paper game. Monte Carlo simulations are performed on a square lattice when varying the temperature and the…
We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We…
Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…
The spatio-temporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatio-temporal patterns arising from the cyclic competition between…
A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle…
The cyclically dominated voter model on a square lattice is extended by taking into consideration the variation of Potts energy during the nearest neighbor invasions. We have investigated the effect of surface tension on the self-…
We study the non-equilibrium steady states that emerge when two interacting three-dimensional Potts blocks slide on each other. As at equilibrium the Potts model exhibits different types of phase transitions for different numbers $q$ of…
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit…
We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group…
The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
In a network of coupled oscillators, a symmetry-broken dynamical state characterized by the coexistence of coherent and incoherent parts can spontaneously form. It is known as a chimera state. We study chimera states in a network consisting…
The importance of triplet states in the photorelaxation dynamics of SO2 is studied by mixed quantum-classical dynamics simulations. Using the Surface Hopping including ARbitrary Couplings (Sharc) method, intersystem crossing processes…
We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are the possible spin values (or colors). The resulting energy landscape is thus significantly…
This study examines the domain-growth dynamics of $q$-state active Potts models ($q=3$--$8$) under the cyclically symmetric conditions using Monte Carlo simulations on square and hexagonal lattices. By imposing active cyclic flipping of…