2011, Zakharova, A., Kurths, J., Vadivasova, T., Koseska, A.

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.

2017, Wu, J., Xu, Y., Ma, J.

As the fluctuations of the internal bioelectricity of nervous system is various and complex, the external electromagnetic radiation induced by magnet flux on membrane can be described by the non-Gaussian type distribution of Levy noise. Thus, the electrical activities in an improved Hindmarsh-Rose model excited by the external electromagnetic radiation of Levy noise are investigated and some interesting modes of the electrical activities are exhibited. The external electromagnetic radiation of Levy noise leads to the mode transition of the electrical activities and spatial phase, such as from the rest state to the firing state, from the spiking state to the spiking state with more spikes, and from the spiking state to the bursting state. Then the time points of the firing state versus Levy noise intensity are depicted. The increasing of Levy noise intensity heightens the neuron firing. Also the stationary probability distribution functions of the membrane potential of the neuron induced by the external electromagnetic radiation of Levy noise with different intensity, stability index and skewness papremeters are analyzed. Moreover, through the positive largest Lyapunov exponent, the parameter regions of chaotic electrical mode of the neuron induced by the external electromagnetic radiation of Levy noise distribution are detected.

2022, Yarragolla, Sahitya, Du, Nan, Hemke, Torben, Zhao, Xianyue, Chen, Ziang, Polian, Ilia, Mussenbrock, Thomas

With the advent of the Internet of Things, nanoelectronic devices or memristors have been the subject of significant interest for use as new hardware security primitives. Among the several available memristors, BiFeO3 (BFO)-based electroforming-free memristors have attracted considerable attention due to their excellent properties, such as long retention time, self-rectification, intrinsic stochasticity, and fast switching. They have been actively investigated for use in physical unclonable function (PUF) key storage modules, artificial synapses in neural networks, nonvolatile resistive switches, and reconfigurable logic applications. In this work, we present a physics-inspired 1D compact model of a BFO memristor to understand its implementation for such applications (mainly PUFs) and perform circuit simulations. The resistive switching based on electric field-driven vacancy migration and intrinsic stochastic behaviour of the BFO memristor are modelled using the cloud-in-a-cell scheme. The experimental current–voltage characteristics of the BFO memristor are successfully reproduced. The response of the BFO memristor to changes in electrical properties, environmental properties (such as temperature) and stress are analyzed and consistant with experimental results.

2013, Hellen, E.H., Dana, S.K., Kurths, J., Kehler, E., Sinha, S.

We report the experimental verification of noise-enhanced logic behaviour in an electronic analog of a synthetic genetic network, composed of two repressors and two constitutive promoters. We observe good agreement between circuit measurements and numerical prediction, with the circuit allowing for robust logic operations in an optimal window of noise. Namely, the input-output characteristics of a logic gate is reproduced faithfully under moderate noise, which is a manifestation of the phenomenon known as Logical Stochastic Resonance. The two dynamical variables in the system yield complementary logic behaviour simultaneously. The system is easily morphed from AND/NAND to OR/NOR logic.

2017, Serdukova, L., Zheng, Y., Duan, J., Kurths, J.

For the tipping elements in the Earth's climate system, the most important issue to address is how stable is the desirable state against random perturbations. Extreme biotic and climatic events pose severe hazards to tropical rainforests. Their local effects are extremely stochastic and difficult to measure. Moreover, the direction and intensity of the response of forest trees to such perturbations are unknown, especially given the lack of efficient dynamical vegetation models to evaluate forest tree cover changes over time. In this study, we consider randomness in the mathematical modelling of forest trees by incorporating uncertainty through a stochastic differential equation. According to field-based evidence, the interactions between fires and droughts are a more direct mechanism that may describe sudden forest degradation in the south-eastern Amazon. In modeling the Amazonian vegetation system, we include symmetric α-stable Lévy perturbations. We report results of stability analysis of the metastable fertile forest state. We conclude that even a very slight threat to the forest state stability represents Ĺevy noise with large jumps of low intensity, that can be interpreted as a fire occurring in a non-drought year. During years of severe drought, high-intensity fires significantly accelerate the transition between a forest and savanna state.

2012, Schewe, Jacob, Levermann, Anders

Indian monsoon rainfall is vital for a large share of the world's population. Both reliably projecting India's future precipitation and unraveling abrupt cessations of monsoon rainfall found in paleorecords require improved understanding of its stability properties. While details of monsoon circulations and the associated rainfall are complex, full-season failure is dominated by large-scale positive feedbacks within the region. Here we find that in a comprehensive climate model, monsoon failure is possible but very rare under pre-industrial conditions, while under future warming it becomes much more frequent. We identify the fundamental intraseasonal feedbacks that are responsible for monsoon failure in the climate model, relate these to observational data, and build a statistically predictive model for such failure. This model provides a simple dynamical explanation for future changes in the frequency distribution of seasonal mean all-Indian rainfall. Forced only by global mean temperature and the strength of the Pacific Walker circulation in spring, it reproduces the trend as well as the multidecadal variability in the mean and skewness of the distribution, as found in the climate model. The approach offers an alternative perspective on large-scale monsoon variability as the result of internal instabilities modulated by pre-seasonal ambient climate conditions.

2020, Zahari, Finn, Pérez, Eduardo, Mahadevaiah, Mamathamba Kalishettyhalli, Kohlstedt, Hermann, Wenger, Christian, Ziegler, Martin

Biological neural networks outperform current computer technology in terms of power consumption and computing speed while performing associative tasks, such as pattern recognition. The analogue and massive parallel in-memory computing in biology differs strongly from conventional transistor electronics that rely on the von Neumann architecture. Therefore, novel bio-inspired computing architectures have been attracting a lot of attention in the field of neuromorphic computing. Here, memristive devices, which serve as non-volatile resistive memory, are employed to emulate the plastic behaviour of biological synapses. In particular, CMOS integrated resistive random access memory (RRAM) devices are promising candidates to extend conventional CMOS technology to neuromorphic systems. However, dealing with the inherent stochasticity of resistive switching can be challenging for network performance. In this work, the probabilistic switching is exploited to emulate stochastic plasticity with fully CMOS integrated binary RRAM devices. Two different RRAM technologies with different device variabilities are investigated in detail, and their potential applications in stochastic artificial neural networks (StochANNs) capable of solving MNIST pattern recognition tasks is examined. A mixed-signal implementation with hardware synapses and software neurons combined with numerical simulations shows that the proposed concept of stochastic computing is able to process analogue data with binary memory cells. © 2020, The Author(s).