LINEAR RECURSION FORMULAS OF GENERALIZED FOCUS QUANTITIES AND LOCAL INTEGRABILITY FOR A CLASS OF THREE-DIMENSIONAL SYSTEMS

Qinlong Wang; Wenyu Li; Wentao Huang

doi:10.11948/20220178

2022 Volume 12 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(3): 1186-1194

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Qinlong Wang, Wenyu Li, Wentao Huang. LINEAR RECURSION FORMULAS OF GENERALIZED FOCUS QUANTITIES AND LOCAL INTEGRABILITY FOR A CLASS OF THREE-DIMENSIONAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(3): 1186-1194. doi: 10.11948/20220178

Citation:

Qinlong Wang, Wenyu Li, Wentao Huang. LINEAR RECURSION FORMULAS OF GENERALIZED FOCUS QUANTITIES AND LOCAL INTEGRABILITY FOR A CLASS OF THREE-DIMENSIONAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2022, 12(3): 1186-1194. doi: 10.11948/20220178

LINEAR RECURSION FORMULAS OF GENERALIZED FOCUS QUANTITIES AND LOCAL INTEGRABILITY FOR A CLASS OF THREE-DIMENSIONAL SYSTEMS

1.
School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China
2.
Center for Applied Mathematics of Guangxi, College of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China

Dedicated to Professor Jibin Li on the occasion of his 80th birthday.
Corresponding author: Email: huangwentao@163.com(W. Huang)
Fund Project: The authors were supported by National Natural Science Foundation of China (12061016, 12161023) and Nature Science Foundation of Guangxi (2020GXNSFAA159138), and Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation

Abstract

Abstract

In this paper, the local integrability of a class of three-dimensional systems is studied. The recursive formulas to compute the generalized focus quantities of the system are deduced firstly, then they are applied to a Lotka-Volterra system. The integrable conditions of the system are obtained and the local integrability is solved completely. The algorithm corresponding to the above formulas is an extension and development of the power series method for the planar differential systems with $ p:-q $ arbitrary resonant saddle point and also readily done with using computer algebra system such as Mathematica or Maple.
- Three-dimensional system /
- integrability /
- power series method /
- generalized focus quantity
MSC: 34C

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References

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