An externally modulated, noise-driven switch for the regulation of SPI1 in Salmonella enterica serovar Typhimurium.

In this work we consider the regulation system present on the SPI1 pathogenicity island of Salmonella enterica serovar Typhimurium. It is well-known that HilA is the central regulator in the overall scheme of SPI1 regulation and directly binds to virulence operons and activates their expression. The regulation of the expression of HilA is via a complex feed-forward loop involving three transcriptional activators: HilC, HilD and RtsA, and the negative regulator HilE. Our aim is to model this regulation network and study its dynamical behavior. We show that this regulatory system can display a bistable behavior relevant to the biology of Salmonella, and that noise can be a driving force in this system.

Blinking Networks of Memristor Oscillatory Circuits in the Flux-Charge Domain.

Multistability phenomena and complex nonlinear dynamics in memristor oscillators pave the way to obtain efficient solutions to optimization problems by means of novel computational architectures based on the interconnection of single-device oscillators. It is well-known that topological properties of interconnections permit to control synchronization and spatio-temporal patterns in oscillatory networks. When the interconnections can change in time with a given probability to connect two oscillators, the whole network acts as a complex network with blinking couplings. The work of has shown that a particular class of blinking complex networks are able to completely synchronize in a faster fashion with respect to other coupling strategies. This work focuses on the specific class of blinking complex networks made of Memristor-based Oscillatory Circuits (MOCs). By exploiting the recent Flux-Charge Analysis Method, we make clear that synchronization phenomena in blinking networks of memristor oscillators having stochastic couplings, i.e., Blinking Memristor Oscillatory Networks (BMONs), correspond to global periodic oscillations on invariant manifolds and the effect of a blinking link is to shift the nonlinear dynamics through the infinite (invariant) manifolds. Numerical simulations performed on MOCs prove that synchronization phenomena can be controlled just by changing the coupling amongst them.

On the study of cellular nonlinear networks via amplitude and phase dynamics.

The purpose of this manuscript is to propose a method for investigating the global dynamics of nonlinear oscillatory networks, with arbitrary couplings. The procedure is based on the assumption that each oscillator can be accurately described via its time-varying amplitude and phase variables. The proposed method allows one to derive a set of coupled nonlinear ordinary differential equations governing this couple of variables. By analyzing the evolution of amplitudes and phases, one can investigate the stability properties of the limit cycles for the whole system in a simpler way with respect to the latest available methodologies. Furthermore, it is proved that this technique also works for weakly connected oscillatory networks. Finally, as a case study, a chain of third-order oscillators (Chua's circuits) is considered and the results are compared to those obtained via a numerical technique, entirely based on the harmonic balance (HB) approach.

A multi-base harmonic balance method applied to Hodgkin-Huxley model.

Our aim is to propose a new robust and manageable technique, called multi-base harmonic balance method, to detect and characterize the periodic solutions of a nonlinear dynamical system. Our case test is the Hodgkin-Huxley model, one of the most realistic neuronal models in literature. This system, depending on the value of the external stimuli current, exhibits periodic solutions, both stable and unstable.