On a discretization process of fractional-order Logistic differential equation | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 22, Issue 3, October 2014, Pages 407-412 PDF (2.03 M) | ||
| Document Type: Original Article | ||
| Authors | ||
| Z.F. El Raheem; S.M. Salman | ||
| Faculty of Education, Alexandria University, Alexandria, Egypt | ||
| Abstract | ||
| In this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant arguments and we apply the proposed discretization on it. The stability of the fixed points of the resultant dynamical system and the Lyapunov exponent are investigated. Finally, we study some dynamic behavior of the resultant systems such as bifurcation and chaos. | ||
| Keywords | ||
| Logistic differential equation; Piecewise constant arguments; Fractional-order differential equations; Fixed points; Lyapunov exponent; Bifurcation | ||
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