Abstract
This paper is concerned with the existence and asymptotic behavior of traveling wave fronts for a food-limited population model with spatio-temporal delay. Using geometric singular perturbation theory and Fredholm alternative, we establish the existence of traveling wave fronts of this model for sufficiently small time delay. The approach is to reformulate the problem as an existence question for a heteroclinic connection in \({\mathbb {R}}^6\). Furthermore, employing standard asymptotic theory, we obtain the asymptotic behavior of traveling wave fronts of this model for the first time.
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Acknowledgements
The authors gratefully acknowledged the anonymous referee for helpful comments and suggestions. Research was supported by the National Natural Science Foundation of China (Grant Nos. 71690242, 91546118 and 11501253), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20140525), and the Major Project of Natural Science Foundation of Jiangsu Province Colleges and Universities (Grant No. 14KJA110001), and the Senior Talents Foundation of Jiangsu University (Grant No. 15JDG083), and the Advantages of Jiangsu Province and the Innovation Project for Graduate Student Research of Jiangsu Province KYLX16_0899.
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Wei, J., Tian, L., Zhou, J. et al. Existence and asymptotic behavior of traveling wave fronts for a food-limited population model with spatio-temporal delay. Japan J. Indust. Appl. Math. 34, 305–320 (2017). https://doi.org/10.1007/s13160-017-0244-1
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DOI: https://doi.org/10.1007/s13160-017-0244-1