No abstract

Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds. © 2009 American Institute of Physics. ͓doi:10.1063/1.3247349͔Nonmonotonic flows with reverse shear are observed in many physical systems. Much previous research indicates that transport properties of such systems can be well described by area preserving maps. Many examples exist, e.g., in the fields of fluid mechanics and plasma physics; in particular, in models that describe zonal flows that occur in geophysics, atmospheric science, and fusion plasma physics. The standard nontwist map (SNM) is a well-known paradigm for investigating transport in reverse shear systems. The nonmonotonicity property of the SNM gives rise to transport barriers due to robust tori (invariant curves) that occur in zonal flows. These tori separate regions of the two-dimensional phase space. Moreover, the influence of these barriers on the transport remains even after the breakup of the tori. This phenomenon, i.e., the difficulty encountered in crossing broken barriers, is explained by examining the stickiness of orbits that occur in some regions of the map phase space. For a certain range of control parameters, these regions emerge near resonances. The presence of stickiness is closely related to the structure of the stable and unstable manifolds of hyperbolic orbits, becoming prevalent when the manifolds reconnect and change from a dominant homoclinic tangle to a combination that includes both homoclinic and heteroclinic tangles.

Neuronal systems have been modelled by complex networks in different description levels. Recently, it has been verified that networks can simultaneously exhibit one coherent and other incoherent domain, known as chimera states. In this work, we study the existence of chimera-like states in a network considering the connectivity matrix based on the cat cerebral cortex. The cerebral cortex of the cat can be separated in 65 cortical areas organised into the four cognitive regions: visual, auditory, somatosensory-motor and frontolimbic. We consider a network where the local dynamics is given by the Hindmarsh-Rose model. The Hindmarsh-Rose equations are a well known model of neuronal activity that has been considered to simulate membrane potential in neuron. Here, we analyse under which conditions chimera-like states are present, as well as the affects induced by intensity of coupling on them. We identify two different kinds of chimera-like states: spiking chimera-like with desynchronised spikes, and bursting chimera-like with desynchronised bursts. Moreover, we find that chimera-like states with desynchronised bursts are more robust to neuronal noise than with desynchronised spikes.

Excessively high, neural synchronization has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronization mechanisms can thus help control or even treat epilepsy. In this paper, we study neural synchronization in a random network where nodes are neurons with excitatory and inhibitory synapses, and neural activity for each node is provided by the adaptive exponential integrate-and-fire model. In this framework, we verify that the decrease in the influence of inhibition can generate synchronization originating from a pattern of desynchronized spikes. The transition from desynchronous spikes to synchronous bursts of activity, induced by varying the synaptic coupling, emerges in a hysteresis loop due to bistability where abnormal (excessively high synchronous) regimes exist. We verify that, for parameters in the bistability regime, a square current pulse can trigger excessively high (abnormal) synchronization, a process that can reproduce features of epileptic seizures. Then, we show that it is possible to suppress such abnormal synchronization by applying a small-amplitude external current on > 10% of the neurons in the network. Our results demonstrate that external electrical stimulation not only can trigger synchronous behavior, but more importantly, it can be used as a means to reduce abnormal synchronization and thus, control or treat effectively epileptic seizures.

In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. These barriers have been identified in symplectic nontwist maps that model such zonal flows. We use the so-called nontwist standard map, a paradigmatic example of nontwist systems, to analyze the parameter dependence of the transport through a broken shearless barrier. On varying a proper control parameter, we identify the onset of structures with high stickness that give rise to an effective barrier near the broken shearless curve. Moreover, we show how these stickness structures, and the concomitant transport reduction in the shearless region, are determined by a homoclinic tangle of the remaining dominant twin island chains. We use the finite-time rotation number, a recently proposed diagnostic, to identify transport barriers that separate different regions of stickness. The identified barriers are comparable to those obtained by using finite-time Lyapunov exponents.

Shearless transport barriers appear in confined plasmas due to non-monotonic radial profiles and cause localized reduction of transport even after they have been broken. In this paper we summarize our recent theoretical and experimental research on shearless transport barriers in plasmas confined in toroidal devices. In particular, we discuss shearless barriers in Lagrangian magnetic field line transport caused by non-monotonic safety factor profiles. We also discuss evidence of particle transport barriers found in the TCABR Tokamak (University of São Paulo) and the Texas Helimak (University of Texas at Austin) in biased discharges with non-monotonic plasma flows.

Lagrangian coherent structures are effective barriers, sticky regions, that separate phase space regions of different dynamical behavior. The usual way to detect such structures is via finite-time Lyapunov exponents. We show that similar results can be obtained for single-frequency systems from finite-time rotation numbers, which are much faster to compute. We illustrate our claim by considering examples of continuous and discrete-time dynamical systems of physical interest.

Chimera states, characterised by coexistence of coherence and incoherence in coupled dynamical systems, have been found in various physical systems, such as mechanical oscillator networks and Josephsonjunction arrays. We used recurrence plots to provide graphical representations of recurrent patterns and identify chimera states. Moreover, we show that recurrence plots can be used as a diagnostic of chimera states and also to identify the chimera collapse.