Explosive first-order transition to synchrony in networked chaotic oscillators

Critical phenomena in complex networks, and the emergence of dynamical abrupt transitions in the macroscopic state of the system are currently a subject of the outmost interest. We report evidence of an explosive phase synchronization in networks of chaotic units. Namely, by means of both extensive simulations of networks made up of chaotic units, and validation with an experiment of electronic circuits in a star configuration, we demonstrate the existence of a first order transition towards synchronization of the phases of the networked units. Our findings constitute the first prove of this kind of synchronization in practice, thus opening the path to its use in real-world applications.Comment: Phys. Rev. Lett. in pres

Dynamics of a ring of three unidirectionally coupled Duffing oscillators with time-dependent damping

We study dynamics of a ring of three unidirectionally coupled double-well Duffing oscillators for three different values of the damping coefficient: fixed dumping, proportional to time, and inversely proportional to time. The dynamics in all cases is analyzed through time series, Fourier and Hilbert transforms, Poincar\'e sections, as well as bifurcation diagrams and Lyapunov exponents with respect to the coupling strength. In the first case, we observe a well-known route from a stable steady state to hyperchaos through Hopf bifurcation and a series of torus bifurcations, as the coupling strength is increased. In the second case, the system is highly dissipative and converges into one of stable equilibria. Finally, in the third case, transient toroidal hyperchaos takes place

Coherence enhancement in coupled chaotic neurons

Through numerical simulations and electronic experiments we demonstrate the improved regularity in inter-spike intervals of a chaotic Hindmarsh-Rose neuron affected by another chaotic neuron

Chaos in Neural Oscillators Induced by Unidirectional Electrical Coupling

We demonstrate that unidirectional electrical coupling between two periodically spiking Hindmarsh-Rose neurons induces bistability in the system. We find that for certain values of intermediate coupling, the slave neuron exhibits coexistence of two attractors. One of them is the periodic orbit similar to the original attractor without coupling, and the other one is a chaotic attractor or a periodic orbit with higher periodicity, depending on the coupling strength. For strong coupling, the slave neuron is monostable at a periodic orbit similar to the attractor of the master neuron. When the master and slave neurons are in a similar attractor they are completely synchronized, whereas being in different states they are in generalized synchronization. We also present the experimental evidence of this behavior with electronic circuits based on the Hindmarsh-Rose model

Multistability and noise-induced transitions in the model of bidirectionally coupled neurons with electrical synaptic plasticity

We systematically study the effects of synaptic plasticity in the model describing dynamics of electrically coupled neuron cells. Neurotransmission through electrical synapses plays an important role in the spike synchrony among neurons in the neural network. Synaptic plasticity is known to arise from the transjunction voltage-dependent conductance of channels formed, for instance, by Connexin-36 (Cx36), the principal gap junction protein of electrical synapses between inhibitory interneurons in vertebrates. A coupling strength between neurons is modulated in a complex manner, and the significance of this regulation in the presence of a stimulus that changes the firing properties of the coupled neurons, is still unknown. The neuron model based on the FitzHung–Nagumo equations exhibits multistability when two neurons are linearly bidirectionally coupled, i.e., two new resting states emerge in addition to the original either resting or spiking state depending on the ionic currents, observed in the solitary neuron. Synaptic plasticity of electrical neurotransmission is accounted in the model by making the coupling strength a linear function of the transjunction current so that the coupling becomes quadratic. This nonlinearity in synaptic transmission results in very rich dynamics leading to chaos in the neuron spikes via a cascade of period-doubling bifurcations as the external current is changed, as well as to amplitude-dependent signal attenuation similar to a low-pass signal filtering effect. The latter property of electrical synapses is consistent with experimental data involving Cx36-mediated electrical communication. In the presence of multiplicative noise, inherent to neural systems, intermittent transitions between the coexisting states occur. In the case of linear coupling, the transjunctional current switches between three states, whereas nonlinearity in coupling destroys one of the coexisting states so that multistate intermittency is converted into on-off intermittency. These results are consistent with physiological experiments on random switches between different states of a single gap junction channel

Family of Bistable Attractors Contained in an Unstable Dissipative Switching System Associated to a SNLF

This work presents a multiscroll generator system, which addresses the issue by the implementation of 9-level saturated nonlinear function, SNLF, being modified with a new control parameter that acts as a bifurcation parameter. By means of the modification of the newly introduced parameter, it is possible to control the number of scrolls to generate. The proposed system has richer dynamics than the original, not only presenting the generation of a global attractor; it is capable of generating monostable and bistable multiscrolls. The study of the basin of attraction for the natural attractor generation (9-scroll SNLF) shows the restrictions in the initial conditions space where the system is capable of presenting dynamical responses, limiting its possible electronic implementations

Numerical study of laser synapse connecting Hindmarsh–Rose neurons

We study numerically the dynamics of a system composed of two artificial neurons connected via an erbium-doped fiber laser. In our system, the laser acts as an optical synapse whose dynamics is controlled with a signal generated by a presynaptic Hindmarsh–Rose neuron, while the laser output drives a postsynaptic Hindmarsh–Rose neuron. Depending on the laser parameter, the postsynaptic neuron can be turned to different dynamical regimes including silence, tonic spikes, bursts with different number of spikes, and chaos