Oscillatory reactive dynamics on surfaces: a lattice limit cycle model

Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities

We study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a Hopf bifurcation. This dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions. The complexity of the dynamics arises from the presence of a limit cycle and four fixed points. When the bifurcation parameter increases away from the Hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes, followed by long resting periods. We observe chimera states in this spiking regime as a coexistence of coherence (synchronization) and incoherence (desynchronization) in a one-dimensional ring with nonlocal coupling and demonstrate that their multiplicity depends on both the system and the coupling parameters. We also show that hierarchical (fractal) coupling topologies induce traveling multichimera states. The speed of motion of the coherent and incoherent parts along the ring is computed through the Fourier spectra of the corresponding dynamics.

Nonequilibrium chemistry in confined environments: a lattice Brusselator model

In this work, we study the effect of molecular crowding on a typical example of a chemical oscillator: the Brusselator model. We adopt to this end a nonequilibrium thermodynamic description, in which the size of particles is introduced via a lattice gas model. The impenetrability and finite volume of the species are shown to affect both the reaction rates and the diffusion terms in the evolution equations for the concentrations. The corrected scheme shows a more complex dynamical behavior than its ideal counterpart, including bistability and excitability. These results help to shed light on recent experimental and computational studies in biochemistry and surface chemistry, in which it was shown that confined environments may greatly affect chemical dynamics.