Collective excitability in highly diluted random networks of oscillators.

We report on collective excitable events in a highly diluted random network of non-excitable nodes. Excitability arises thanks to a self-sustained local adaptation mechanism that drives the system on a slow timescale across a hysteretic phase transition involving states with different degrees of synchronization. These phenomena have been investigated for the Kuramoto model with bimodal distribution of the natural frequencies and for the Kuramoto model with inertia and a unimodal frequency distribution. We consider global and partial stimulation protocols and characterize the system response for different levels of dilution. We compare the results with those obtained in the fully coupled case showing that such collective phenomena are remarkably robust against network diluteness.

Emergent excitability in populations of nonexcitable units.

Population bursts in a large ensemble of coupled elements result from the interplay between the local excitable properties of the nodes and the global network topology. Here, collective excitability and self-sustained bursting oscillations are shown to spontaneously emerge in globally coupled populations of nonexcitable units subject to adaptive coupling. The ingredients to observe collective excitability are the coexistence of states with different degrees of synchronization joined to a global feedback acting, on a slow timescale, against the synchronization (desynchronization) of the oscillators. These regimes are illustrated for two paradigmatic classes of coupled rotators, namely, the Kuramoto model with and without inertia. For the bimodal Kuramoto model we analytically show that the macroscopic evolution originates from the existence of a critical manifold organizing the fast collective dynamics on a slow timescale. Our results provide evidence that adaptation can induce excitability by maintaining a network permanently out of equilibrium.

Plant shoots exhibit synchronized oscillatory motions.

In animals, the ability to move has evolved as an important means of protection from predators and for enhancing nutrient uptake. In the animal kingdom, an individual's movements may become coordinated with those of other individuals that belong to the same group, which leads, for example, to the beautiful collective patterns that are observed in flocks of birds and schools of fish or in animal migration. Land plants, however, are fixed to the ground, which limits their movement and, apparently, their interactions and collective behaviors. We show that emergent maize plants grown in a group exhibit synchronized oscillatory motions that may be in-phase or anti-phase. These oscillations occur in short bursts and appear when the leaves rupture from the coleoptile tip. The appearance of these oscillations indicates an abrupt increase in the plant growth rate, which may be associated with a sudden change in the energy uptake for photosynthesis. Our results suggest that plant shoots behave as a complex network of biological oscillators, interacting through biophysical links, e.g. chemical substances or electric signals.

Resting electrical network activity in traps of the aquatic carnivorous plants of the genera Aldrovanda and Utricularia.

In this study the MEA (multielectrode array) system was used to record electrical responses of intact and halved traps, and other trap-free tissues of two aquatic carnivorous plants, Aldrovanda vesiculosa and Utricularia reflexa. They exhibit rapid trap movements and their traps contain numerous glands. Spontaneous generation of spikes with quite uniform shape, propagating across the recording area, has been observed for all types of sample. In the analysis of the electrical network, higher richer synchronous activity was observed relative to other plant species and organs previously described in the literature: indeed, the time intervals between the synchronized clusters (the inter-spike intervals) create organized patterns and the propagation times vary non-linearly with the distance due to this synchronization. Interestingly, more complex electrical activity was found in traps than in trap-free organs, supporting the hypothesis that the nature of the electrical activity may reflect the anatomical and functional complexity of different organs. Finally, the electrical activity of functionally different traps of Aldrovanda (snapping traps) and Utricularia (suction traps) was compared and some differences in the features of signal propagation were found. According to these results, a possible use of the MEA system for the study of different trap closure mechanisms is proposed.

Anticipated synchronization in coupled complex Ginzburg-Landau systems.

We study the occurrence of anticipated synchronization in two complex Ginzburg-Landau systems coupled in a master-slave configuration. Master and slave systems are ruled by the same autonomous function, but the slave system receives the injection from the master and is subject to a negative delayed self-feedback loop. We give evidence that the magnitude of the largest anticipation time, obtained for complex-valued coupling constants, depends on the dynamical regime where the system operates (defect turbulence, phase turbulence, or bichaos) and scales with the linear autocorrelation time of the system. We also provide analytical conditions for the stability of the anticipated synchronization manifold that are in qualitative agreement with those obtained numerically. Finally, we report on the existence of anticipated synchronization in coupled two-dimensional complex Ginzburg-Landau systems.

The electrical network of maize root apex is gravity dependent.

Investigations carried out on maize roots under microgravity and hypergravity revealed that gravity conditions have strong effects on the network of plant electrical activity. Both the duration of action potentials (APs) and their propagation velocities were significantly affected by gravity. Similarly to what was reported for animals, increased gravity forces speed-up APs and enhance synchronized electrical events also in plants. The root apex transition zone emerges as the most active, as well as the most sensitive, root region in this respect.

Electrical spiking in bacterial biofilms.

In nature, biofilms are the most common form of bacterial growth. In biofilms, bacteria display coordinated behaviour to perform specific functions. Here, we investigated electrical signalling as a possible driver in biofilm sociobiology. Using a multi-electrode array system that enables high spatio-temporal resolution, we studied the electrical activity in two biofilm-forming strains and one non-biofilm-forming strain. The action potential rates monitored during biofilm-forming bacterial growth exhibited a one-peak maximum with a long tail, corresponding to the highest biofilm development. This peak was not observed for the non-biofilm-forming strain, demonstrating that the intensity of the electrical activity was not linearly related to the bacterial density, but was instead correlated with biofilm formation. Results obtained indicate that the analysis of the spatio-temporal electrical activity of bacteria during biofilm formation can open a new frontier in the study of the emergence of collective microbial behaviour.

Experimental study of firing death in a network of chaotic FitzHugh-Nagumo neurons.

The FitzHugh-Nagumo neurons driven by a periodic forcing undergo a period-doubling route to chaos and a transition to mixed-mode oscillations. When coupled, their dynamics tend to be synchronized. We show that the chaotically spiking neurons change their internal dynamics to subthreshold oscillations, the phenomenon referred to as firing death. These dynamical changes are observed below the critical coupling strength at which the transition to full chaotic synchronization occurs. Moreover, we find various dynamical regimes in the subthreshold oscillations, namely, regular, quasiperiodic, and chaotic states. We show numerically that these dynamical states may coexist with large-amplitude spiking regimes and that this coexistence is characterized by riddled basins of attraction. The reported results are obtained for neurons implemented in the electronic circuits as well as for the model equations. Finally, we comment on the possible scenarios where the coupling-induced firing death could play an important role in biological systems.

Origin of polar order in dense suspensions of phototactic micro-swimmers.

A main question for the study of collective motion in living organisms is the origin of orientational polar order, i.e., how organisms align and what are the benefits of such collective behaviour. In the case of micro-organisms swimming at a low Reynolds number, steric repulsion and long-range hydrodynamic interactions are not sufficient to explain a homogeneous polar order state in which the direction of motion is aligned. An external symmetry-breaking guiding field such as a mechanism of taxis appears necessary to understand this phonemonon. We have investigated the onset of polar order in the velocity field induced by phototaxis in a suspension of a motile micro-organism, the algae Chlamydomonas reinhardtii, for density values above the limit provided by the hydrodynamic approximation of a force dipole model. We show that polar order originates from a combination of both the external guiding field intensity and the population density. In particular, we show evidence for a linear dependence of a phototactic guiding field on cell density to determine the polar order for dense suspensions and demonstrate the existence of a density threshold for the origin of polar order. This threshold represents the density value below which cells undergoing phototaxis are not able to maintain a homogeneous polar order state and marks the transition to ordered collective motion. Such a transition is driven by a noise dominated phototactic reorientation where the noise is modelled as a normal distribution with a variance that is inversely proportional to the guiding field strength. Finally, we discuss the role of density in dense suspensions of phototactic micro-swimmers.

Swarming behavior in plant roots.

Interactions between individuals that are guided by simple rules can generate swarming behavior. Swarming behavior has been observed in many groups of organisms, including humans, and recent research has revealed that plants also demonstrate social behavior based on mutual interaction with other individuals. However, this behavior has not previously been analyzed in the context of swarming. Here, we show that roots can be influenced by their neighbors to induce a tendency to align the directions of their growth. In the apparently noisy patterns formed by growing roots, episodic alignments are observed as the roots grow close to each other. These events are incompatible with the statistics of purely random growth. We present experimental results and a theoretical model that describes the growth of maize roots in terms of swarming.

Synaptic plasticity modulates autonomous transitions between waking and sleep states: insights from a Morris-Lecar model.

The transitions between waking and sleep states are characterized by considerable changes in neuronal firing. During waking, neurons fire tonically at irregular intervals and a desynchronized activity is observed at the electroencephalogram. This activity becomes synchronized with slow wave sleep onset when neurons start to oscillate between periods of firing (up-states) and periods of silence (down-states). Recently, it has been proposed that the connections between neurons undergo potentiation during waking, whereas they weaken during slow wave sleep. Here, we propose a dynamical model to describe basic features of the autonomous transitions between such states. We consider a network of coupled neurons in which the strength of the interactions is modulated by synaptic long term potentiation and depression, according to the spike time-dependent plasticity rule (STDP). The model shows that the enhancement of synaptic strength between neurons occurring in waking increases the propensity of the network to synchronize and, conversely, desynchronization appears when the strength of the connections become weaker. Both transitions appear spontaneously, but the transition from sleep to waking required a slight modification of the STDP rule with the introduction of a mechanism which becomes active during sleep and changes the proportion between potentiation and depression in accordance with biological data. At the neuron level, transitions from desynchronization to synchronization and vice versa can be described as a bifurcation between two different states, whose dynamical regime is modulated by synaptic strengths, thus suggesting that transition from a state to an another can be determined by quantitative differences between potentiation and depression.

Predict-prevent control method for perturbed excitable systems.

We present a control method based on two steps: prediction and prevention. For prediction we use the anticipated synchronization scheme, considering unidirectional coupling between excitable systems in a master-slave configuration. The master is the perturbed system to be controlled, meanwhile the slave is an auxiliary system which is used to predict the master's behavior. The prevention is obtained by sending a control signal to the master system, which temporarily lowers its excitability threshold and prevents its future reaction to the external perturbation. We demonstrate theoretically and experimentally that an efficient control may be achieved.

Control of transient synchronization with external stimuli.

A network of coupled chaotic oscillators can switch spontaneously to a state of collective synchronization at some critical coupling strength. We show that for a locally coupled network of units with coexisting quiescence and chaotic spiking states, set slightly below the critical coupling value, the collective excitable or bistable states of synchronization arise in response to a stimulus applied to a single node. We provide an explanation of this behavior and show that it is due to a combination of the dynamical properties of a single node and the coupling topology. By the use of entropy as a collective indicator, we present a new method for controlling the transient synchronization.

Dynamical mechanism of anticipating synchronization in excitable systems.

We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirectional delayed coupling which are subject to the same external forcing. We demonstrate for different paradigms of excitable system that, due to the coupling, the excitability threshold for the slave system is always lower than that for the master. As a consequence the two systems respond to a common external forcing with different response times. This allows us to explain in a simple way the mechanism behind the phenomenon of anticipating synchronization in excitable systems.