Stability analysis of the five-dimensional energy demand-supply system

Kun-Yi Yang; Chun Xia An

Kybernetika (2021)

  • Volume: 57, Issue: 5, page 750-775
  • ISSN: 0023-5954

Abstract

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In this paper, a five-dimensional energy demand-supply system has been considered. On the one hand, we analyze the stability for all of the equilibrium points of the system. For each of equilibrium point, by analyzing the characteristic equation, we show the conditions for the stability or instability using Routh-Hurwitz criterion. Then numerical simulations have been given to illustrate all of cases for the theoretical results. On the other hand, by introducing the phenomenon of time delay, we establish the five-dimensional energy demand-supply model with time delay. Then we analyze the stability of the equilibrium points for the delayed system by the stability switching theory. Especially, Hopf bifurcation has been considered by showing the explicit formulae using the central manifold theorem and Poincare normalization method. For each cases of the theorems including the Hopf bifurcation, numerical simulations have been given to illustrate the effectiveness of the main results.

How to cite

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Yang, Kun-Yi, and An, Chun Xia. "Stability analysis of the five-dimensional energy demand-supply system." Kybernetika 57.5 (2021): 750-775. <http://eudml.org/doc/298126>.

@article{Yang2021,
abstract = {In this paper, a five-dimensional energy demand-supply system has been considered. On the one hand, we analyze the stability for all of the equilibrium points of the system. For each of equilibrium point, by analyzing the characteristic equation, we show the conditions for the stability or instability using Routh-Hurwitz criterion. Then numerical simulations have been given to illustrate all of cases for the theoretical results. On the other hand, by introducing the phenomenon of time delay, we establish the five-dimensional energy demand-supply model with time delay. Then we analyze the stability of the equilibrium points for the delayed system by the stability switching theory. Especially, Hopf bifurcation has been considered by showing the explicit formulae using the central manifold theorem and Poincare normalization method. For each cases of the theorems including the Hopf bifurcation, numerical simulations have been given to illustrate the effectiveness of the main results.},
author = {Yang, Kun-Yi, An, Chun Xia},
journal = {Kybernetika},
keywords = {energy demand-supply; equilibrium points; stability; hopf bifurcation},
language = {eng},
number = {5},
pages = {750-775},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stability analysis of the five-dimensional energy demand-supply system},
url = {http://eudml.org/doc/298126},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Yang, Kun-Yi
AU - An, Chun Xia
TI - Stability analysis of the five-dimensional energy demand-supply system
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 5
SP - 750
EP - 775
AB - In this paper, a five-dimensional energy demand-supply system has been considered. On the one hand, we analyze the stability for all of the equilibrium points of the system. For each of equilibrium point, by analyzing the characteristic equation, we show the conditions for the stability or instability using Routh-Hurwitz criterion. Then numerical simulations have been given to illustrate all of cases for the theoretical results. On the other hand, by introducing the phenomenon of time delay, we establish the five-dimensional energy demand-supply model with time delay. Then we analyze the stability of the equilibrium points for the delayed system by the stability switching theory. Especially, Hopf bifurcation has been considered by showing the explicit formulae using the central manifold theorem and Poincare normalization method. For each cases of the theorems including the Hopf bifurcation, numerical simulations have been given to illustrate the effectiveness of the main results.
LA - eng
KW - energy demand-supply; equilibrium points; stability; hopf bifurcation
UR - http://eudml.org/doc/298126
ER -

References

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