Coherent structures emerging from turbulence in the nonlocal complex Ginzburg-Landau equation

Amplitude-mediated chimera states

We investigate the possibility of obtaining chimera state solutions of the nonlocal complex Ginzburg-Landau equation (NLCGLE) in the strong coupling limit when it is important to retain amplitude variations. Our numerical studies reveal the existence of a variety of amplitude-mediated chimera states (including stationary and nonstationary two-cluster chimera states) that display intermittent emergence and decay of amplitude dips in their phase incoherent regions. The existence regions of the single-cluster chimera state and both types of two-cluster chimera states are mapped numerically in the parameter space of C(1) and C(2), the linear and nonlinear dispersion coefficients, respectively, of the NLCGLE. They represent a new domain of dynamical behavior in the well-explored rich phase diagram of this system. The amplitude-mediated chimera states may find useful applications in understanding spatiotemporal patterns found in fluid flow experiments and other strongly coupled systems.

Normal-form approach to spatiotemporal pattern formation in globally coupled electrochemical systems

We show that the experimental global coupling (GC) of spatially extended electrochemical oscillators is weak close to a supercritical Hopf bifurcation. A center manifold reduction allows then the normal form which comprises the GC and the naturally existing nonlocal (migration) coupling (NLC) to be derived. We show that the interaction between NLC and GC widens the spectrum of coherent structures found in globally coupled oscillatory media and allows for wavelength selection of standing waves, stabilization of phase clusters without breaking phase invariance, and creation of heteroclinic networks connecting families of oscillatory states characterized by different spatial symmetries.