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Lag bifurcation analysis method based on multi-scale time-delay neural network

A neural network and analysis method technology, applied in the field of time-delay neural network bifurcation phenomenon analysis, can solve the problems of cumbersome process and large amount of calculation, and achieve the effects of simplified solution, good consistency and reduced cost

Pending Publication Date: 2020-08-18
DONGHUA UNIV
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  • Claims
  • Application Information

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Problems solved by technology

To study the properties of the periodic solution of Hopf bifurcation, the central manifold reduction method and the normative theory are usually used. This method is relatively complete in theory, but the process is cumbersome and the amount of calculation is large.

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  • Lag bifurcation analysis method based on multi-scale time-delay neural network
  • Lag bifurcation analysis method based on multi-scale time-delay neural network
  • Lag bifurcation analysis method based on multi-scale time-delay neural network

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Embodiment Construction

[0013] The present invention will be further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the teachings of the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of this application.

[0014] The invention provides a multi-scale time-delay neural network lag bifurcation analysis method including the following steps:

[0015] Step 1. Transform the original model and establish a new state space equation of zero equilibrium point;

[0016] Step 2. Use the multi-scale method to perform non-linear expansion at the Hopf bifurcation point, redefine bifurcation parameters, and slow down the time scale. 0 (T 0 = T) and slow scale T 2...

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Abstract

The invention relates to a lag bifurcation analysis method based on a multi-scale time delay neural network. Compared with some traditional methods, the solution of a nonlinear equation can be simplified; only a third-order Stuart-Landau equation needs to be derived, the change of the oscillation amplitude near the bifurcation point can be described, the analytical expression of the position of the bistable region and the amplitude of the unstable and stable limit ring can be obtained through the five-order Stuart-Landau equation, and meanwhile, the solution of the Start-Landau equation is much faster than the solution of the whole nonlinear system. According to the method, the cost for researching oscillation and subcritical phenomena near the Hopf bifurcation in numerical simulation andexperiments can be reduced, and the method has good consistency with complete nonlinear analysis.

Description

Technical field [0001] The invention relates to a method for analyzing the lag bifurcation phenomenon of a time-delay neural network based on multiple scales, and belongs to the field of analyzing the bifurcation phenomenon of a time-delay neural network. Background technique [0002] At present, in the study of the dynamic properties of neural network systems, some typical artificial neural network models are used to reveal the mechanism of various complex dynamic behaviors caused by time lag, so as to better understand the law of neural activity. Very important work. Time lag often leads to instability of the system's motion, resulting in various forms of bifurcation. Among the bifurcations of nonlinear time-delay dynamic systems, Hopf bifurcation is universal and the most widely discussed. To study the properties of Hopf bifurcation periodic solutions, the central manifold reduction method and the canonical type theory are usually used. The method is relatively complete in t...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/27G06N3/04
CPCG06F30/27G06N3/049G06N3/045
Inventor 于航任正云
Owner DONGHUA UNIV