**10. Conclusion**

where

**Figure 3.**

**Figure 4.**

**78**

*A t*ð Þ¼ , *x t*ð Þ, *y t*ð Þ 0*:*5*e*

*B t*ð Þ¼ , *x t*ð Þ, *y t*ð Þ 0*:*5*e*

*E t*ð Þ¼� , *x t*ð Þ, *y t*ð Þ 0*:*5*e*

*C t*ð Þ¼� , *x t*ð Þ, *y t*ð Þ *<sup>e</sup>*�*<sup>t</sup>*

*D t*ð Þ¼ , *x t*ð Þ, *y t*ð Þ *<sup>e</sup>*�*<sup>t</sup>*

*Numerical simulation 1 for solution of Eq.(44).*

*Numerical simulation 2 for solution of Eq.(44).*

�*y t*ð Þ*x t*ð Þ *<sup>y</sup>*<sup>2</sup>

*Advances in Dynamical Systems Theory, Models, Algorithms and Applications*

�*y t*ð Þ *x t*ð Þ*<sup>e</sup>*

*x t*ð Þ*e*

�*y t*ð Þ *y*<sup>2</sup>

ðÞ�*t* 2*y t*ð Þ*e* �*y t*ð Þ <sup>2</sup>

*x t*ð Þ*x*�<sup>1</sup> ð Þ*t*

*<sup>e</sup>*�*y t*ð Þ *<sup>y</sup>*<sup>2</sup> ð Þ ð Þ�*<sup>t</sup>* <sup>2</sup>*y t*ð Þ *ex t*ð Þ*x*�1ðÞ�*<sup>t</sup>* <sup>2</sup>*y t*ð Þ*e*�*y t*ð Þ � *ex t*ð Þ*x*�2ðÞþ*<sup>t</sup> <sup>y</sup>*2ð Þ*<sup>t</sup> <sup>e</sup>*�*y t*ð Þ ,

*<sup>e</sup>x t*ð Þ *<sup>x</sup>*�1ðÞ�*<sup>t</sup> <sup>x</sup>*�<sup>2</sup> ð Þ ð Þ*<sup>t</sup> ex t*ð Þ*x*�1ðÞ�*<sup>t</sup>* <sup>2</sup>*y t*ð Þ*e*�*y t*ð Þ � *ex t*ð Þ*x*�2ðÞþ*<sup>t</sup> <sup>y</sup>*2ð Þ*<sup>t</sup> <sup>e</sup>*�*y t*ð Þ ,

ðÞ�*<sup>t</sup>* <sup>2</sup>*y t*ð Þ <sup>1</sup> � *<sup>x</sup>*�<sup>1</sup>

*x t*ð Þ � *<sup>e</sup>*

,

<sup>2</sup> � <sup>4</sup>*y t*ð Þþ *<sup>y</sup>*<sup>2</sup> ð Þ*<sup>t</sup>* ,

ð Þþ*<sup>t</sup> x t*ðÞ� <sup>2</sup> <sup>þ</sup> <sup>2</sup>*x*�<sup>1</sup> ð Þ*<sup>t</sup> :*

(43)

The invariant method widens horizons for constructing and researching into mathematical models of real systems with the invariants that hold out under any strong random disturbances.
