Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators

We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.Comment: postprint, as accepted in Chaos, 10 pages, 7 figure

Geometry of heteroclinic cascades in scalar parabolic differential equations

We investigate the geometrical properties of the attractor for semilinear scalar parabolic PDEs on a bounded interval with Neumann boundary conditions. Using the nodal properties of the stationary solutions which are determined by an ordinary boundary value problem, we obtain crucial information about the long-time behavior for the full PDE. Especially, we prove a criterion for the intersection of strong- stable and unstable manifolds in the finite dimensional Morse-Smale flow on the attractor

The Turing bifurcation in network systems: Collective patterns and single differentiated nodes

We study the emergence of patterns in a diffusively coupled network that undergoes a Turing instability. Our main focus is the emergence of stable solutions with a single differentiated node in systems with large and possibly irregular network topology. Based on a mean-field approach, we study the bifurcations of such solutions for varying system parameters and varying degree of the differentiated node. Such solutions appear typically before the onset of Turing instability and provide the basis for the complex scenario of multistability and hysteresis that can be observed in such systems. Moreover, we discuss the appearance of stable collective patterns and present a codimension-two bifurcation that organizes the interplay between collective patterns and patterns with single differentiated nodes

Lipid sensing and lipid sensors: Cytoplasmic fatty acid binding protein sensing fatty acids for peroxisome proliferator activated receptor activation

Abstract.: Translation of nutrient stimuli through intracellular signaling is important for adaption and regulation of metabolic processes, while deregulation by either genetic or environmental factors predisposes towards the development of metabolic disorders. Besides providing energy, fatty acids act as prominent signaling molecules by altering cell membrane structures, affecting the lipid modification status of proteins, and by modulating ligand-activated nuclear receptor activity. Given their highly hydrophobic nature, fatty acids in the aqueous intracellular compartment are bound to small intracellular lipid binding proteins which function as intracellular carriers of these hydrophobic components. This review describes recent advances in identifying intracellular pathways for cytosolic fatty acid signaling through ligand activated receptors by means of small intracellular lipid binding proteins. The mechanism behind intracellular fatty acid transport and subsequent nuclear receptor activation is an emerging concept, and advances in understanding this process provide new potential therapeutic targets towards the treatment of metabolic disorder