Influence of sinusoidal forcing on the master FitzHugh-Nagumo neuron model and global dynamics of a unidirectionally coupled two-neuron system.

In this paper, we investigate a seven-parameter, five-dimensional dynamical system, specifically a unidirectional coupling of two FitzHugh-Nagumo neuron models, with one neuron being sinusoidally driven. This master-slave configuration features neuron N1 as the master, subjected to an external sinusoidal electrical current, and neuron N2 as the slave, interacting with N1 through an electrical force. We report numerical results for three distinct scenarios where N1 operates in (i) periodic, (ii) quasiperiodic, and (iii) chaotic regimes.

Multistability for nonlinear acoustic-gravity waves in a rotating atmosphere.

The multistable states of low-frequency, short-wavelength nonlinear acoustic-gravity waves propagating in a small slope with respect to the vertical ones are explored in a rotating atmosphere. The bifurcation patterns en route to irregular behaviors and the long-term dynamics of the low-order nonlinear model system are studied for varying air Prandtl number σ between 0.5 and 1.

Periodicity suppression in continuous-time dynamical systems by external forcing.

We investigate periodicity suppression by an external periodic forcing in different flows, each modeled by a set of three autonomous nonlinear first-order ordinary differential equations. By varying the amplitude of a sinusoidal forcing with a fixed angular frequency, we show through numerical simulations, including parameter planes plots, phase-space portraits, and the largest Lyapunov exponent, that windows of periodicity embedded in chaotic regions may be totally suppressed.

Hopfield neural network: the hyperbolic tangent and the piecewise-linear activation functions.

This paper reports two-dimensional parameter-space plots for both, the hyperbolic tangent and the piecewise-linear neuron activation functions of a three-dimensional Hopfield neural network. The plots obtained using both neuron activation functions are compared, and we show that similar features are present on them. The occurrence of self-organized periodic structures embedded in chaotic regions is verified for the two cases.

Lyapunov exponent diagrams of a 4-dimensional Chua system.

We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos.

Some two-dimensional parameter spaces of a Chua system with cubic nonlinearity.

In this paper we investigate three two-dimensional parameter spaces of a three-parameter set of autonomous differential equations used to model the Chua oscillator, where the piecewise-linear function usually taken to describe the nonlinearity of the Chua diode has been replaced by a cubic polynomial. It is made by using three independent two-dimensional cross sections of the three-dimensional parameter space generated by the model, which contains three parameters. We show that, independent of the parameter set considered in plots, all the diagrams present periodic structures embedded in a large chaotic region, and we also show that these structures organize themselves in period-adding cascades.

Basin size evolution between dissipative and conservative limits.

Recent methods for stabilizing systems like, e.g., loss-modulated CO2 lasers, involve inducing controlled monostability via slow parameter modulations.