University of Tabriz Computational Methods for Differential Equations 2345-3982 12 2 2024 03 01 Synchronization a chaotic system with Quadratic terms using the contraction Method 361 373 16884 10.22034/cmde.2023.55987.2337 EN Marzieh Pabasteh Department of Mathematics, Payame Noor University, Tehran, Iran. Bashir Naderi Department of Mathematics, Payame Noor University, Tehran, Iran. Hasan Zarei Department of Mathematics, Payame Noor University, Tehran, Iran Journal Article 2023 03 31 In this article, Synchronization and control methods are discussed as essential topics in science. The contraction method is an exciting method that has been studied for the synchronization of chaotic systems with known and unknown parameters. The controller and the dynamic parameter estimation are obtained using the contraction theory to prove the stability of the synchronization error and the low parameter estimation. The control scheme does not employ the Lyapunov method. For demonstrate the ability of the proposed method, we performed a numerical simulation and compared the result with the previous literature. https://cmde.tabrizu.ac.ir/article_16884_ee0658a8b2c07311f312bc9b6dc27a7a.pdf