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Homoclinic and Heteroclinic Motions in Economic Models with Exogenous Shocks

Marat Akhmet

Marat Akhmet

Department of Mathematics, Middle East Technical UniversityAnkara, Turkey
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Akhmet, Marat
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Mehmet Onur Fen

Mehmet Onur Fen

Neuroscience Institute, Georgia State UniversityAtlanta, USA
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Onur Fen, Mehmet
  
Jan 01, 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
© 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.
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).
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).
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).
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