<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Differential equation modelling was earlier used to discover better and understand various biological phenomena and social problems. We hope to understand the stability of the system and the Hopf bifurcation based on the characteristic roots of the linear system. Because group competitive sports require participants to have certain competitive skills, those who do not have sports skills but want to develop into activities must receive training and specific training. Therefore, based on the research background, the article proposes a time-lag group competitive martial arts activity model with a time lag effect. Through delay differential equation theory and Hopf bifurcation theory, the stability of the equilibrium point and the existence of periodic solutions generated by the Hopf bifurcation caused by the ‘instability’ of the equilibrium point are discussed. Finally, the theoretical results are simulated and verified with the help of MATLAB software.</p>
</abstract>

Differential equation modelling was earlier used to discover better and understand various biological phenomena and social problems. We hope to understand the stability of the system and the Hopf bifurcation based on the characteristic roots of the linear system. Because group competitive sports require participants to have certain competitive skills, those who do not have sports skills but want to develop into activities must receive training and specific training. Therefore, based on the research background, the article proposes a time-lag group competitive martial arts activity model with a time lag effect. Through delay differential equation theory and Hopf bifurcation theory, the stability of the equilibrium point and the existence of periodic solutions generated by the Hopf bifurcation caused by the ‘instability’ of the equilibrium point are discussed. Finally, the theoretical results are simulated and verified with the help of MATLAB software.

Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts

Physical Education Teaching and Research Section

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Differential equation modelling was earlier used to discover better and understand various biological phenomena and social problems. We hope to understand the...

Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts

Publicado en línea: 30 dic 2021

Páginas: 207 - 214

Recibido: 17 jun 2021

Aceptado: 24 sept 2021

DOI: https://doi.org/10.2478/amns.2021.2.00152

Palabras clave
group competitive martial arts activities, balance point, stability, time lag, Hopf bifurcation, numerical simulation

© 2021 Shuang Chen et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts

Publicado en línea: 30 dic 2021

Páginas: 207 - 214

Recibido: 17 jun 2021

Aceptado: 24 sept 2021

DOI: https://doi.org/10.2478/amns.2021.2.00152

Palabras clavegroup competitive martial arts activities, balance point, stability, time lag, Hopf bifurcation, numerical simulation

© 2021 Shuang Chen et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Palabras clave
group competitive martial arts activities, balance point, stability, time lag, Hopf bifurcation, numerical simulation