2,817 research outputs found
Stability analysis of a hypothalamic-pituitary-adrenal axis model with inclusion of glucocorticoid receptor and memory
This paper analyzes a four-dimensional model of the
hypothalamic-pituitary-adrenal (HPA) axis that includes the influence of the
glucocorticoid receptor in the pituitary. Due to the spatial separation between
the hypothalamus, pituitary and adrenal glands, distributed time delays are
introduced in the mathematical model. The existence of the positive equilibrium
point is proved and a local stability and bifurcation analysis is provided,
considering several types of delay kernels. The fractional-order model with
discrete time delays is also taken into account. Numerical simulations are
provided to illustrate the effectiveness of the theoretical findings.Comment: 9 page
On the validity of memristor modeling in the neural network literature
An analysis of the literature shows that there are two types of
non-memristive models that have been widely used in the modeling of so-called
"memristive" neural networks. Here, we demonstrate that such models have
nothing in common with the concept of memristive elements: they describe either
non-linear resistors or certain bi-state systems, which all are devices without
memory. Therefore, the results presented in a significant number of
publications are at least questionable, if not completely irrelevant to the
actual field of memristive neural networks
Recent Advances and Applications of Fractional-Order Neural Networks
This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed
Synchronization of fractional chaotic complex networks with delays
summary:The synchronization of fractional-order complex networks with delay is investigated in this paper. By constructing a novel Lyapunov-Krasovskii function and taking integer derivative instead of fractional derivative of the function, a sufficient criterion is obtained in the form of linear matrix inequalities to realize synchronizing complex dynamical networks. Finally, a numerical example is shown to illustrate the feasibility and effectiveness of the proposed method
Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks
In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks
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