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Applied Mathematics and Nonlinear Sciences
Volume 1 (2016): Issue 1 (January 2016)
Open Access
Homoclinic and Heteroclinic Motions in Economic Models with Exogenous Shocks
Marat Akhmet
Marat Akhmet
and
Mehmet Onur Fen
Mehmet Onur Fen
| Jan 01, 2016
Applied Mathematics and Nonlinear Sciences
Volume 1 (2016): Issue 1 (January 2016)
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Published Online:
Jan 01, 2016
Page range:
1 - 10
Received:
Jun 01, 2015
Accepted:
Oct 25, 2015
DOI:
https://doi.org/10.21042/AMNS.2016.1.00001
Keywords
Exogenous shocks
,
Homoclinic and heteroclinic motions
,
Stable and unstable sets
,
Kaldor model
© 2016 Marat Akhmet, Mehmet Onur Fen, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
Fig. 1
The trajectory of system (7) corresponding to the initial data y(0) = 0.014 and k(0) = −0.025. The solution of (8) with d0 = 0.18 is used in the simulation.
Fig. 2
The homoclinic solution of (9). The bounded solutions ϕc(t) and ϕd* (t) are depicted in blue and red colors, respectively. It seen in the figure that ϕc(t) is homoclinic to ϕd* (t).
Fig. 3
The heteroclinic solution of (9). The bounded solutions ϕc¯(t)$\begin{array}{} \displaystyle \phi_{\overline{c}}(t) \end{array}$, ϕd* (t) and ϕd** (t) are depicted in blue, red and green colors, respectively. The simulation demonstrates that ϕc¯(t)$\begin{array}{} \displaystyle \phi_{\overline{c}}(t) \end{array}$ is heteroclinic to ϕd* (t), ϕd** (t).