Delayed dynamics in an electronic relaxation oscillator.

We present an experimental investigation of the complex dynamics of a modulated relaxation oscillator implemented by using a unipolar junction transistor (UJT) showing the transition to chaos through torus breakdown. In a previous paper a continuous model was introduced for the same system, explaining chaos based on analogy with a memristor. We propose here a new approach based on a piecewise linear model with delay considering a measured parasitic delay effect. The inclusion of this delay, accounting for memory effects, increases the dimensionality of the model, allowing the transition to chaos as observed in the experiment. The piecewise delayed model shows analogies with a two-dimensional leaky integrate-and-fire model used in neurodynamics.

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.

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.

Phenomenology of consciousness from apprehension to judgment.

We explore two different moments of human cognition, namely apprehension (A), whereby a coherent perception emerges by recruitment of large neuron groups and judgment (B), whereby memory retrieval of different (A) units coded in a suitable language and comparison of them leads to the formulation of a judgment. The first one has a duration around 1 sec (from 0.5 to 3 sec), it appears as an a-temporal present and its neural correlate is a wide synchronization in the EEG gamma band. It may be described as an interpretation of sensorial stimuli in terms of some stored algorithm, via a Bayes procedure. The second one entails the comparison of two apprehensions acquired at different times, coded in a given language, and retrieved by memory. It lasts around 3 sec and requires self-consciousness, as the judging agent must be well aware that he/she is the same one who faces the two coded apprehensions under scrutiny in order to extract a mutual relation. At variance with (A), (B) does not presuppose an algorithm, but it rather builds a new behavioural model by an inverse Bayes procedure. It will be shown how this build up of a novel model is related to creativity and free will.

Introduction to focus issue: nonlinear dynamics in cognitive and neural systems.

In this Focus Issue, two interrelated concepts, namely, deterministic chaos and cognitive abilities, are discussed.

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.

Control and synchronization of laser bursting and its implications in neuroscience.

We present experimental and numerical evidence of control and synchronization of burst events in modulated CO(2) lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model display the frequency locking of bursts in a suitable interval of coupling strengths. The analogy with neuronal bursting will also be discussed in view of the role of bursting synchronization in cognitive functions.

Attractor selection in a modulated laser and in the Lorenz circuit.

By tuning a control parameter, a chaotic system can either display two or more attractors (generalized multistability) or exhibit an interior crisis, whereby a chaotic attractor suddenly expands to include the region of an unstable orbit (bursting regime).Recently, control of multistability and bursting have been experimentally proved in a modulated class B laser by means of a feedback method. In a bistable regime, the method relies on the knowledge of the frequency components of the two attractors. Near an interior crisis, the method requires retrieval of the unstable orbit colliding with the chaotic attractor. We also show that a suitable parameter modulation is able to control bistability in the Lorenz system. We observe that, for every given modulation frequency, the chaotic attractor is destroyed under a boundary crisis. The threshold control amplitude depends on the control frequency and the location of the operating point in the bistable regime. Beyond the boundary crisis, the system remains in the steady state even if the control is switched off, demonstrating control of bistability.

Synchronization of spontaneous bursting in a CO2 laser.

We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.

Predicting phase synchronization in a spiking chaotic CO2 laser.

An approach is presented for the reconstruction of phase synchronization phenomena in a chaotic CO2 laser from experimental data. We analyze this laser system in a regime able to phase synchronize with a weak sinusoidal forcing. Our technique recovers the synchronization diagram of the experimental system from only few measurement data sets, thus allowing the prediction of the regime of phase synchronization as well as nonsynchronization in a broad parameter space of forcing frequency and amplitude without further experiments.