Quantifying Geobacter sulfurreducens growth: A mathematical model based on acetate concentration as an oxidizing substrate.

We developed a mathematical model to simulate dynamics associated with the proliferation of Geobacter and ultimately optimize cellular operation by analyzing the interaction of its components. The model comprises two segments: an initial part comprising a logistic form and a subsequent segment that incorporates acetate oxidation as a saturation term for the microbial nutrient medium. Given that four parameters can be obtained by minimizing the square root of the mean square error between experimental Geobacter growth and the mathematical model, the model underscores the importance of incorporating nonlinear terms. The determined parameter values closely align with experimental data, providing insights into the mechanisms that govern Geobacter proliferation. Furthermore, the model has been transformed into a scaleless equation with only two parameters to simplify the exploration of qualitative properties. This allowed us to conduct stability analysis of the fixed point and construct a co-dimension two bifurcation diagram.

Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator.

In this paper, we propose using paraxial matrix optics to describe a ring-phase conjugated resonator that includes an intracavity chaos-generating element; this allows the system to behave in phase space as a Bogdanov Map. Explicit expressions for the intracavity chaos-generating matrix elements were obtained. Furthermore, computer calculations for several parameter configurations were made; rich dynamic behavior among periodic orbits high periodicity and chaos were observed through bifurcation diagrams. These results confirm the direct dependence between the parameters present in the intracavity chaos-generating element.

Separation of coexisting dynamical regimes in multistate intermittency based on wavelet spectrum energies in an erbium-doped fiber laser.

We propose a method for the detection and localization of different types of coexisting oscillatory regimes that alternate with each other leading to multistate intermittency. Our approach is based on consideration of wavelet spectrum energies. The proposed technique is tested in an erbium-doped fiber laser with four coexisting periodic orbits, where external noise induces intermittent switches between the coexisting states. Statistical characteristics of multistate intermittency, such as the mean duration of the phases for every oscillation type, are examined with the help of the developed method. We demonstrate strong advantages of the proposed technique over previously used amplitude methods.

Critical slowing down and noise-induced intermittency in bistable perception: bifurcation analysis.

Stochastic dynamics and critical slowing down were studied experimentally and numerically near the onset of dynamical bistability in visual perception under the influence of noise. Exploring the Necker cube as the essential example of an ambiguous figure, and using its wire contrast as a control parameter, we measured dynamical hysteresis in two coexisting percepts as a function of both the velocity of the parameter change and the background luminance. The bifurcation analysis allowed us to estimate the level of cognitive noise inherent to brain neural cells activity, which induced intermittent switches between different perception states. The results of numerical simulations with a simple energy model are in good qualitative agreement with psychological experiments.

Experimental implementation of a biometric laser synaptic sensor.

We fabricate a biometric laser fiber synaptic sensor to transmit information from one neuron cell to the other by an optical way. The optical synapse is constructed on the base of an erbium-doped fiber laser, whose pumped diode current is driven by a pre-synaptic FitzHugh-Nagumo electronic neuron, and the laser output controls a post-synaptic FitzHugh-Nagumo electronic neuron. The implemented laser synapse displays very rich dynamics, including fixed points, periodic orbits with different frequency-locking ratios and chaos. These regimes can be beneficial for efficient biorobotics, where behavioral flexibility subserved by synaptic connectivity is a challenge.

Knowledge discovery in spectral data by means of complex networks.

In the last decade, complex networks have widely been applied to the study of many natural and man-made systems, and to the extraction of meaningful information from the interaction structures created by genes and proteins. Nevertheless, less attention has been devoted to metabonomics, due to the lack of a natural network representation of spectral data. Here we define a technique for reconstructing networks from spectral data sets, where nodes represent spectral bins, and pairs of them are connected when their intensities follow a pattern associated with a disease. The structural analysis of the resulting network can then be used to feed standard data-mining algorithms, for instance for the classification of new (unlabeled) subjects. Furthermore, we show how the structure of the network is resilient to the presence of external additive noise, and how it can be used to extract relevant knowledge about the development of the disease.

Rogue waves in a multistable system.

Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon. The results of numerical simulations are in good agreement with experiments.

Synchronization of coupled bistable chaotic systems: experimental study.

We carried out an experimental study of the synchronization of two unidirectionally coupled Rössler-like electronic circuits with two coexisting chaotic attractors. Different stages of synchronization are identified on the route from asynchronous motion to complete synchronization, as the coupling parameter is increased: intermittent asynchronous jumps between coexisting attractors; intermittent anticipating phase synchronization; and generalized synchronization in the form of subharmonic entrainment terminated by complete synchronization. All these regimes are analysed with time-series, power spectra and phase-space plots of the drive and response oscillators. The experimental study implicitly confirms the results of numerical simulations.