Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T09:20:28.755Z Has data issue: false hasContentIssue false
  • English
  • Français

DYNAMICS OF PSEUDO ALMOST PERIODIC SOLUTION FOR IMPULSIVE NEOCLASSICAL GROWTH MODEL

Part of: Qualitative theory

Published online by Cambridge University Press:  06 March 2017

ZHINAN XIA Open the ORCID record for ZHINAN XIA [Opens in a new window]
ZHINAN XIA*
Affiliation:
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang, 310023, China email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper analyses the pseudo almost periodicity of the impulsive neoclassical growth model. We investigate the existence, uniqueness and exponential stability of the pseudo almost periodic solution. Moreover, an example is given to illustrate the significance of the main findings.

Keywords

pseudo almost periodic solutionneoclassical growth modelcontraction mapping principleexponential stability

MSC classification

Primary: 34C27: Almost and pseudo-almost periodic solutions
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 359 - 367
Copyright
© 2017 Australian Mathematical Society 

References

Alonso, A. I., Hong, J. and Rojo, J., “A class of ergodic solutions of differential equations with piecewise constant arguments”, Dynam. Systems Appl. 7 (1998) 561–574; http://wmatem.eis.uva.es/∼jesroj/papers_a/ergodi_a.html.Google Scholar
Alzabut, J. O., “Almost periodic solutions for an impulsive delay Nicholson’s blowflies model”, J. Comput. Appl. Math. 234 (2010) 233–239; doi:10.1016/j.cam.2009.12.019.CrossRefGoogle Scholar
Alzabut, J. O., Stamov, G. T. and Sermutlu, E., “On almost periodic solutions for an impulsive delay logarithmic population model”, Math. Comput. Modelling 51 (2010) 625–631; doi:10.1016/j.mcm.2009.11.001.CrossRefGoogle Scholar
Chen, W. and Liu, B. W., “Positive almost periodic solution for a class of Nicholson’s blowflies model with multiple time-varying delays”, J. Comput. Appl. Math. 235 (2011) 2090–2097; doi:10.1016/j.cam.2010.10.007.CrossRefGoogle Scholar
Chen, W. and Wang, W. T., “Global exponential stability for a delay differential neoclassical growth model”, Adv. Difference Equ. 2014 (2014) 325, 1–9; doi:10.1186/1687-1847-2014-325.CrossRefGoogle Scholar
Chérif, F., “Pseudo almost periodic solution of Nicholson’s blowflies model with mixed delays”, Appl. Math. Model. 39 (2015) 5152–5163; doi:10.1016/j.apm.2015.03.043.CrossRefGoogle Scholar
Day, R., “Irregular growth cycles”, Amer. Econ. Rev. 72 (1982) 406–414; http://www.jstor.org/stable/1831540.Google Scholar
Day, R., “The emergence of chaos from classical economic growth”, Q. J. Econ. 98 (1983) 203–213; http://www.jstor.org/stable/1885621.CrossRefGoogle Scholar
Diagana, T., “Stepanov-like pseudo-almost periodicity and its applications to some nonautonomous differential equations”, Nonlinear Anal. 69 (2008) 4277–4285; doi:10.1016/j.na.2007.10.051.CrossRefGoogle Scholar
Ding, H. S. and Nieto, J. J., “A new approach for positive almost periodic solutions to a class of Nicholson’s blowflies model”, J. Comput. Appl. Math. 253 (2013) 249–254; doi:10.1016/j.cam.2013.04.028.CrossRefGoogle Scholar
Fink, A. M., Almost periodic differential equations (Springer, New York, 1974).CrossRefGoogle Scholar
Liu, J. W. and Zhang, C. Y., “Composition of piecewise pseudo almost periodic functions and applications to abstract impulsive differential equations”, Adv. Difference Equ. 2013 (2013) 1–21; doi:10.1186/1687-1847-2013-11.CrossRefGoogle Scholar
Matsumoto, A. and Szidarovszky, F., “Delay differential neoclassical growth model”, J. Econ. Behav. Organ. 78 (2011) 272–289; doi:10.1016/j.jebo.2011.01.014.CrossRefGoogle Scholar
Matsumoto, A. and Szidarovszky, F., “Asymptotic behavior of a delay differential neoclassical growth model”, Sustainability 5 (2013) 440–455; doi:10.3390/su5020440.CrossRefGoogle Scholar
Saker, S. H. and Agarwal, S., “Oscillation and global attractivity in a periodic Nicholson’s blowflies model”, Math. Comput. Modelling 35 (2002) 719–731; doi:10.1016/S0895-7177(02)00043-2.CrossRefGoogle Scholar
Samoilenko, A. M. and Perestyuk, N. A., Impulsive differential equations, Vol. 14 (World Scientific, Singapore, 1995).CrossRefGoogle Scholar
Yao, Z., “Existence and exponential stability of the unique positive almost periodic solution for impulsive Nicholson’s blowflies model with linear harvesting term”, Appl. Math. Model. 39 (2015) 7124–7133; doi:10.1016/j.apm.2015.03.002.CrossRefGoogle Scholar