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Subject: Computer Simulation × WGL Institute: PIK ×

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Now showing 1 - 3 of 3
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    Systems Medicine of Cancer: Bringing Together Clinical Data and Nonlinear Dynamics of Genetic Networks
    (London : Hindawi, 2016) Blyuss, Konstantin B.; Manchanda, Ranjit; Kurths, Jürgen; Alsaedi, Ahmed; Zaikin, Alexey
    Editorial
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    The stability of memristive multidirectional associative memory neural networks with time-varying delays in the leakage terms via sampled-data control
    (San Francisco, California, US : PLOS, 2018) Wang, Weiping; Yu, Xin; Luo, Xiong; Wang, Long; Li, Lixiang; Kurths, Jürgen; Zhao, Wenbing; Xiao, Jiuhong
    In this paper, we propose a new model of memristive multidirectional associative memory neural networks, which concludes the time-varying delays in leakage terms via sampled-data control. We use the input delay method to turn the sampling system into a continuous time-delaying system. Then we analyze the exponential stability and asymptotic stability of the equilibrium points for this model. By constructing a suitable Lyapunov function, using the Lyapunov stability theorem and some inequality techniques, some sufficient criteria for ensuring the stability of equilibrium points are obtained. Finally, numerical examples are given to demonstrate the effectiveness of our results.
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    Lévy noise improves the electrical activity in a neuron under electromagnetic radiation
    (San Francisco, CA : Public Library of Science (PLoS), 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.