وجود هرج و مرج، رفتار دینامیکی با مشتقات مرتبه کسر و هماهنگ سازی تصویری تابع سازگار با پارامترهای نامشخص یک سیستم هرج و مرج

In this article, the authors have studied dynamics of Duffing–Van der Pol system with fractional order derivative and found the existence of chaos. The main contribution of this effort is implementation of the Largest Lyapunov Exponent (LLE) criteria based on Wolf’s algorithm. The conditions for chaos control based on fractional Routh-Hurwitz stability conditions and feedback control are obtained. Also synchronization between fractional order chaotic system and controlled fractional order Duffing–Van der Pol system using modified adaptive function projective synchronization method for different scaling matrix has been obtained. Numerical simulation results which are carried out using Adams–Bashforth–Moulton method show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order systems.