On the Two Methods for Finding 4-Dimensional Duck Solutions

On the Two Methods for Finding 4-Dimensional Duck Solutions

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摘要 This paper gives the existence of a duck solution in a slow-fast system in R2+2 using two ways. One is an indirect way and the other is a direct way. In the indirect way, the original system is once reduced to the slow-fast system in R2+1. In the direct one, it has a 4-dimensional duck solution when having an efficient local model. This is already published in [1,2]. Some sufficient conditions are given to get such a good model. This paper gives the existence of a duck solution in a slow-fast system in R2+2 using two ways. One is an indirect way and the other is a direct way. In the indirect way, the original system is once reduced to the slow-fast system in R2+1. In the direct one, it has a 4-dimensional duck solution when having an efficient local model. This is already published in [1,2]. Some sufficient conditions are given to get such a good model.

作者 Kiyoyuki Tchizawa

机构地区 Institute of Administration Engineering

出处《Applied Mathematics》 2014年第1期16-24,共9页 应用数学（英文）

关键词 Slow-Fast System SINGULAR Perturbation DUCK SOLUTIONS BLOWING-UP NONSTANDARD Analysis Slow-Fast System Singular Perturbation Duck Solutions Blowing-Up Nonstandard Analysis

分类号 O1 [理学—基础数学]

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参考文献1

1Kiyoyuki Tchizawa.On Relative Stability in 4-Dimensional Duck Solution[J].Journal of Mathematics and System Science,2012,2(9):558-563. 被引量：1

二级参考文献9

1K. Tchizawa, On a Local Model for Finding 4-Dimensional Duck Solutions, Selected Topics in Mathematical Methods and Computational Techniques in Electrical Engineering, 2010, pp. 177-183.
2A.K. Zvonkin, M.A. Shubin, Non-standard analysis and singular perturbations of ordinary differential equations, Russian Math. Surveys 39 (1984) 69-131.
3E. Benoit, Canards et enlacements, Publ. Math. IHES 72 (1990), 63-91.
4E. Benoit, Canards en un point pseudo-singulier noeud, Bulletin de la SMF (1999), 2-12.
5S.A. Campbell, M. Waite, Multistability in coupled Fitzhugh-Nagumo oscillators, Nonlinear Analysis 47 (2000) 1093-1104.
6K. Tchizawa, S.A. Campbell, On winding duck solutionsin R4, Proceedings of Neural, Parallel, and Scientific Computations 2 (2002) 315-318.
7N.P. Bhatia, G.P. Szego, Stability Theory of Dynamical Systems, Springer, 161 (1970).
8K. Tchizawa, H. Miki, H. Nishino, On the existence of a duck solution in Goodwin's nonlinear business cycle model, Nonlinear Analysis 63 (2005) e2553-e2558.
9H. Miki, H. Nishino, K. Tchizawa, On the possible occurrence of duck solutions in domestic and two-region business cycle models, Nonlinear Studies 19 (1) (2012) 39-55.

Applied Mathematics

2014年第1期

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On the Two Methods for Finding 4-Dimensional Duck Solutions

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