On a new fractional-order Logistic model with feedback control |
| |
Authors: | Manh Tuan Hoang A.M.Nagy |
| |
Affiliation: | Department of Mathematics,FPT University,Hoa Lac Hi-Tech Park,Km29 Thang Long Blvd,Hanoi,Viet Nam;Kuwait University,Faculty of Science,Department of Mathematics,Safat 13060,Kuwait;Department of Mathematics,Faculty of Science,Benha University,Benha 13518,Egypt |
| |
Abstract: | In this paper, we formulate and analyze a new fractional-order Logistic model with feedback control, which is different from a recognized mathematical model proposed in our very recent work. Asymptotic stability of the proposed model and its numerical solutions are studied rigorously. By using the Lyapunov direct method for fractional dynamical systems and a suitable Lyapunov function, we show that a unique positive equilibrium point of the new model is asymptotically stable. As an important consequence of this, we obtain a new mathematical model in which the feedback control variables only change the position of the unique positive equilibrium point of the original model but retain its asymptotic stability. Furthermore, we construct unconditionally positive nonstandard finite difference(NSFD) schemes for the proposed model using the Mickens' methodology. It is worth noting that the constructed NSFD schemes not only preserve the positivity but also provide reliable numerical solutions that correctly reflect the dynamics of the new fractional-order model. Finally, we report some numerical examples to support and illustrate the theoretical results. The results indicate that there is a good agreement between the theoretical results and numerical ones. |
| |
Keywords: | |
本文献已被 CNKI 万方数据 等数据库收录! |
|