Propagating wave merging in a precipitation reaction

Propagating precipitation waves are a remarkable form of spatiotemporal behavior that arise through the coupling of reaction, diffusion, and precipitation. We study a system with a sodium hydroxide outer electrolyte and an aluminum hydroxide inner electrolyte. In a redissolution Liesegang system, a single propagating precipitation band moves down through the gel, with precipitate formed at the band front and precipitate dissolved at the band back. Complex spatiotemporal waves occur within the propagating precipitation band, including counter-rotating spiral waves, target patterns, and annihilation of waves on collision. We have also carried out experiments in thin slices of gel, which have revealed propagating waves of a diagonal precipitation feature within the primary precipitation band. These waves display a wave merging phenomenon in which two horizontally propagating waves merge into a single wave. Computational modeling permits the development of a detailed understanding of the complex dynamical behavior.

Novel modes of synchronization in star networks of coupled chemical oscillators

Photochemically coupled micro-oscillators are studied experimentally and computationally in star networks to investigate the modes and mechanisms of synchronization. The micro-oscillators are catalyst-loaded beads that are placed in catalyst-free Belousov-Zhabotinsky (BZ) solutions. The properties of the photochemical coupling between the oscillators are determined by the composition of the BZ reaction mixtures, and both excitatory coupling and inhibitory coupling are studied. Synchronization of peripheral oscillators coupled through a hub oscillator is exhibited at coupling strengths leading to novel modes of synchronization of the hub with the peripheral oscillators. A theoretical analysis provides insights into the mechanism of the synchronization. The heterogeneous peripheral oscillators have different phase velocities that give rise to a phase divergence; however, the perturbation from the hub acts to realign the phases by delaying the faster oscillators more than the slower oscillators.

Photochemical motion control of surface active Belousov-Zhabotinsky droplets

Photochemical control of the motion of surface active Belousov-Zhabotinsky (BZ) droplets in an oil-surfactant medium is carried out with illumination intensity gradients. Droplet motion is analyzed under conditions of constant uniform illumination and a constant illumination gradient. Control of droplet motion is developed by testing different illumination gradients. Complex hypotrochoid target trajectories are tracked by BZ droplets illuminated with two-dimensional V-shaped gradients.

Transition from spiral wave chimeras to phase cluster states

Photochemically coupled Belousov-Zhabotinsky micro-oscillators are studied in experiments and simulations. Generally good agreement between the experimental and simulated dynamical behavior is found, with spiral wave chimeras exhibited at small values of the time delay in the coupling between the oscillators, spiral wave core splitting at higher values, and phase cluster states replacing the spiral wave dynamics at the highest values of the time delay. Spiral wave chimera dynamics is exhibited experimentally for much of the time delay range, while spiral wave phase cluster states are exhibited more in the model simulations. In addition to comparing the experimental and simulation behavior, we explore the novel spiral wave phase cluster states and develop a mechanism for this new and unusual dynamical behavior.

Synchronization of heterogeneous oscillator populations in response to weak and strong coupling

Synchronous behavior of a population of chemical oscillators is analyzed in the presence of both weak and strong coupling. In each case, we derive upper bounds on the critical coupling strength which are valid for arbitrary populations of nonlinear, heterogeneous oscillators. For weak perturbations, infinitesimal phase response curves are used to characterize the response to coupling, and graph theoretical techniques are used to predict synchronization. In the strongly perturbed case, we observe a phase dependent perturbation threshold required to elicit an immediate spike and use this behavior for our analytical predictions. Resulting upper bounds on the critical coupling strength agree well with our experimental observations and numerical simulations. Furthermore, important system parameters which determine synchronization are different in the weak and strong coupling regimes. Our results point to new strategies by which limit cycle oscillators can be studied when the applied perturbations become strong enough to immediately reset the phase.

Autonomous cycling between excitatory and inhibitory coupling in photosensitive chemical oscillators

Photochemically coupled Belousov-Zhabotinsky micro-oscillators are studied in experiments and simulations. The photosensitive oscillators exhibit excitatory or inhibitory coupling depending on the surrounding reaction mixture composition, which can be systematically varied. In-phase or out-of-phase synchronization is observed with predominantly excitatory or inhibitory coupling, respectively, and complex frequency cycling between excitatory and inhibitory coupling is found between these extremes. The dynamical behavior is characterized in terms of the corresponding phase response curves, and a map representation of the dynamics is presented.

Chimera and chimera-like states in populations of nonlocally coupled homogeneous and heterogeneous chemical oscillators

Chimera and chimera-like states are characterized in populations of photochemically coupled Belousov-Zhabotinsky (BZ) oscillators. Simple chimeras and chimera states with multiple and traveling phase clusters, phase-slip behavior, and chimera-like states with phase waves are described. Simulations with a realistic model of the discrete BZ system of populations of homogeneous and heterogeneous oscillators are compared with each other and with experimental behavior.

Desynchronization of stochastically synchronized chemical oscillators

Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.

Phase-lag synchronization in networks of coupled chemical oscillators

Chemical oscillators with a broad frequency distribution are photochemically coupled in network topologies. Experiments and simulations show that the network synchronization occurs by phase-lag synchronization of clusters of oscillators with zero- or nearly zero-lag synchronization. Symmetry also plays a role in the synchronization, the extent of which is explored as a function of coupling strength, frequency distribution, and the highest frequency oscillator location. The phase-lag synchronization occurs through connected synchronized clusters, with the highest frequency node or nodes setting the frequency of the entire network. The synchronized clusters successively "fire," with a constant phase difference between them. For low heterogeneity and high coupling strength, the synchronized clusters are made up of one or more clusters of nodes with the same permutation symmetries. As heterogeneity is increased or coupling strength decreased, the phase-lag synchronization occurs partially through clusters of nodes sharing the same permutation symmetries. As heterogeneity is further increased or coupling strength decreased, partial synchronization and, finally, independent unsynchronized oscillations are observed. The relationships between these classes of behavior are explored with numerical simulations, which agree well with the experimentally observed behavior.

Three-dimensional modeling of propagating precipitation waves

A general three-dimensional model for propagating precipitation waves is presented. Structural features identified in experimental studies of propagating waves in the AlCl3/NaOH and NaAl(OH)4/HCl systems are described by the 3D model. Two forms of precipitate with different physical properties play key mechanistic roles in the wave propagation. Experimentally observed circular and spiral waves are simulated by the 3D model, as well as wave annihilation on the collision of two waves.

Insights into collective cell behaviour from populations of coupled chemical oscillators

Biological systems such as yeast show coordinated activity driven by chemical communication between cells. Experiments with coupled chemical oscillators can provide insights into the collective behaviour.

Link weight evolution in a network of coupled chemical oscillators

Link weight evolution is studied in a network of coupled chemical oscillators. Oscillators are perturbed by adjustments in imposed light intensity based on excitatory or inhibitory links to other oscillators undergoing excitation. Experimental and modeling studies demonstrate that the network is capable of producing sustained coordinated activity. The individual nodes of the network exhibit incoherent firing events; however, a dominant frequency can be discerned within the collective signal by Fourier analysis. The introduction of spike-timing-dependent plasticity yields a network that evolves to a stable unimodal link weight distribution.

Propagating precipitation waves: experiments and modeling

Traveling precipitation waves, including counterrotating spiral waves, are observed in the precipitation reaction of AlCl3 with NaOH [Volford, A.; et al. Langmuir 2007, 23, 961 - 964]. Experimental and computational studies are carried out to characterize the wave behavior in cross-section configurations. A modified sol-coagulation model is developed that is based on models of Liesegang band and redissolution systems. The dynamics of the propagating waves is characterized in terms of growth and redissolution of a precipitation feature that travels through a migrating band of colloidal precipitate.

Chimera States in populations of nonlocally coupled chemical oscillators

Chimera states occur spontaneously in populations of coupled photosensitive chemical oscillators. Experiments and simulations are carried out on nonlocally coupled oscillators, with the coupling strength decreasing exponentially with distance. Chimera states with synchronized oscillators, phase waves, and phase clusters coexisting with unsynchronized oscillators are analyzed. Irregular motion of the cores of asynchronous oscillators is found in spiral-wave chimeras.

Emergence of collective behavior in groups of excitable catalyst-loaded particles: spatiotemporal dynamical quorum sensing

Spontaneous spatiotemporal wave activity occurs in groups of excitable particles for groups larger than a critical size. Experiments are carried out with particles loaded with the catalyst of the Belousov-Zhabotinsky reaction that are immersed in catalyst-free reaction mixture. The particles diffusively exchange activator and inhibitor species with the surrounding solution. All particles are nonoscillatory when separated from the other particles; however, target and spiral waves are exhibited in sufficiently large groups. A cellular particle model of the system also exhibits transitions from excitable steady state behavior to spatiotemporal wave activity with increasing group size.

Dynamical quorum sensing and synchronization in large populations of chemical oscillators

Populations of certain unicellular organisms, such as suspensions of yeast in nutrient solutions, undergo transitions to coordinated activity with increasing cell density. The collective behavior is believed to arise through communication by chemical signaling via the extracellular solution. We studied large, heterogeneous populations of discrete chemical oscillators (approximately 100,000) with well-defined kinetics to characterize two different types of density-dependent transitions to synchronized oscillatory behavior. For different chemical exchange rates between the oscillators and the surrounding solution, increasing oscillator density led to (i) the gradual synchronization of oscillatory activity, or (ii) the sudden "switching on" of synchronized oscillatory activity. We analyze the roles of oscillator density and exchange rate of signaling species in these transitions with a mathematical model of the interacting chemical oscillators.

Clusters and switchers in globally coupled photochemical oscillators

We experimentally investigate the transition to synchronization in a population of photochemical oscillators with weak global coupling. Above a critical coupling strength the oscillators join a one-phase group or two-phase clusters. The number of oscillators in each cluster depends on the initial phase distribution, and irregular switching of oscillators between clusters is observed. The fully synchronized state emerges above a second critical coupling strength. In agreement with earlier theory, the experiments demonstrate the importance of population heterogeneity in cluster multistability.

Collective Behavior of a Population of Chemically Coupled Oscillators

Experiments are performed in which a large number (approximately 10(4)) of relaxation oscillators are globally coupled through the concentration of chemicals in the surrounding solution. Each oscillator consists of a microscopic catalyst-loaded particle that displays oscillations in the concentrations of chemical species when suspended in catalyst-free Belousov-Zhabotinsky (BZ) reaction solution. In the absence of stirring, the uncoupled particles display a range of oscillatory frequencies. In the well-stirred system, oscillations appear in the surrounding solution for greater than a critical number density of particles (n(crit)). There is a growth in the amplitude of oscillations with increasing n, accompanied by a slight increase or no change in frequency. A model is proposed to account for the behavior, in which the transfer of activator and inhibitor to and from the bulk medium is considered for each particle. We demonstrate that the appearance and subsequent growth in the amplitude of oscillations may be associated with partial synchronization of the oscillators.

Facilitation of efficient search of an unbaited radial-arm maze in rats by D1, but not D2, dopamine receptors

Dopamine (DA) agonists facilitate and antagonists inhibit conditioned preparatory behaviors in rats. We provide added evidence that increased D1 receptor activation facilitates unconditioned preparatory behavior as well, this time in the form of efficient search of an unbaited radial-arm maze. Administration of 0.1, but not 1.0, mg/kg sc SKF81297, a full D1 agonist, increased the number of novel arms chosen in the first eight arms entered. Treatment with 0.1 mg/kg sc D-amphetamine, an indirect DA agonist, also increased search efficiency when given on the first test day but not when given following a test day with a 1.0 mg/kg dose. The 0.1-mg/kg amphetamine-induced facilitation was blocked by coinjection of 0.005 mg/kg SCH23390, a D1 antagonist. Treatment with quinpirole, a D2 agonist, or eticlopride, a D2 antagonist, decreased amount of maze search, but did not affect efficiency. Collectively, our results support the possibility there is a general facilitatory effect of D1 activation on unconditioned preparatory behavior.

Facilitation of preparatory behavior in an artificial prey paradigm by D1-subfamily dopamine receptor activation

Dopamine agonists facilitate, and antagonists inhibit, conditioned preparatory behaviors in rats. Similar effects are demonstrated on an unconditioned preparatory behavior: predatory search and contact of a moving artificial prey stimulus. Apomorphine (0.1, 0.2 mg/kg), a direct agonist, had no effect relative to a within-subject injection of saline vehicle but d-amphetamine (0.1 mg/kg), an indirect agonist, increased contact frequency without altering overall motor activation. To determine the relative importance of the D1 and D2 subfamilies of receptors in the amphetamine effect, separate groups of animals received amphetamine co-injected with either SCH23390 (0.01 and 0.005 mg/kg) or eticlopride (0.01 mg/kg), D1 and D2 antagonists, respectively. Whereas the eticlopride-amphetamine group showed no change in contact frequency from baseline, co-injections of either dose of SCH23390 and amphetamine led to near total suppression of contact, as did treatment with SCH23390 (0.005 mg/kg) alone. Treatment with 0.01 mg/kg eticlopride alone increased contact frequency while treatment with a higher dose (0.1 mg/kg) had no effect. Treatment with the D1-subfamily agonist SKF81297 (0.1 mg/kg) increased contact frequency. Collectively, these results support the hypothesis that dopamine mediates unconditioned preparatory behavior and suggest differing roles for the D1 and D2 receptor subfamilies.