Complex dynamics induced by a sine nonlinearity in a five-term chaotic system: FPGA hardware design and synchronization.

This paper presents a new five-term chaotic model derived from the Rössler prototype-4 equations. The proposed system is elegant, variable-boostable, multiplier-free, and exclusively based on a sine nonlinearity. However, its algebraic simplicity hides very complex dynamics demonstrated here using familiar tools such as bifurcation diagrams, Lyapunov exponents spectra, frequency power spectra, and basins of attraction. With an adjustable number of equilibrium, the new model can generate infinitely many identical chaotic attractors and limit cycles of different magnitudes. Its dynamic behavior also reveals up to six nontrivial coexisting attractors. Analog circuit and field programmable gate array-based implementation are discussed to prove its suitability for analog and digital chaos-based applications. Finally, the sliding mode control of the new system is investigated and simulated.

Erratum to: Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design.

[This corrects the article DOI: 10.1007/s11571-016-9393-1.].

Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design.

In this paper, we report on the synchronization of a pacemaker neuronal ensemble constituted of an AB neuron electrically coupled to two PD neurons. By the virtue of this electrical coupling, they can fire synchronous bursts of action potential. An external master neuron is used to induce to the whole system the desired dynamics, via a nonlinear controller. Such controller is obtained by a combination of sliding mode and feedback control. The proposed controller is able to offset uncertainties in the synchronized systems. We show how noise affects the synchronization of the pacemaker neuronal ensemble, and briefly discuss its potential benefits in our synchronization scheme. An extended Hindmarsh-Rose neuronal model is used to represent a single cell dynamic of the network. Numerical simulations and Pspice implementation of the synchronization scheme are presented. We found that, the proposed controller reduces the stochastic resonance of the network when its gain increases.

Finite-time synchronization of tunnel-diode-based chaotic oscillators.

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by pspice experiment are presented to show the feasibility of the proposed method.