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{\Large \textbf{Controlbbbbbbbbbbbbbbbbbbbbbb }}\\[3mm]
{\large \textsf{\emph{Marzieh \footnote{$ ^{\star} $Corresponding author (E-mail: b)}}}}
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\begin{abstract}
In this article, we explore the behavior of a chaotic memristor system, with four-dimensional, such as bifurcation and Lyapunov exponent as a chaotic characteristic, for new parameters. Our main goal is to control the system using a graphical algorithm based on contraction method in dynamical systems, which, designed controller by this method is more simple than most controllers for chaotic systems. In this article, we explore the behavior of a chaotic memristor system, with four-dimensional, such as bifurcation and Lyapunov exponent as a chaotic characteristic, for new parameters. Our main goal is to control the system using a graphical algorithm based on contraction method in dynamical systems, which, designed controller by this method is more simple than most controllers for chaotic systems. 
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\noindent\textsf{Keywords:} Contraction theory, 
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\noindent\textsf{2020 }  

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%\section{\bf Definitions and Notations}
\section*{\centerline{1. Definitions and notations}} \label{sec1} \setcounter{section}{1}\setcounter{theorem}{0} 
Chaos is a concept often used for a nonlinear dynamic. Chaos theory is a mathematical tool that extracts beautiful structures from chaos. The origins of chaos theory were introduced by Henri Poincaré in 1908, who attempted to study an unsolved problem of Newtonian Laplacian celestial mechanics (the three-body problem). During this research, Poincaré realized that infinitely complex behavior may exist in nonlinear systems. Chaos theory, firstly discussed by MIT meteorologist Edward Lorenz, who simulated weather patterns on computers in the 1960 \cite{18}. In recent years, deterministic chaos has been seen as a model in electronic circuits, laser technology, cardiology, organizations, financial markets, urban communities, and climate.\\
Chaos is a concept often used for a nonlinear dynamic. Chaos theory is a mathematical tool that extracts beautiful structures from chaos. The origins of chaos theory were introduced by Henri Poincaré in 1908, who attempted to study an unsolved problem of Newtonian Laplacian celestial mechanics (the three-body problem). During this research, Poincaré realized that infinitely complex behavior may exist in nonlinear systems. Chaos theory, firstly discussed by MIT meteorologist Edward Lorenz, who simulated weather patterns on computers in the 1960 \cite{18}. In recent years, deterministic chaos has been seen as a model in electronic circuits, laser technology, cardiology, organizations, financial markets, urban communities, and climate.\\Chaos is a concept often used for a nonlinear dynamic. Chaos theory is a mathematical tool that extracts beautiful structures from chaos. The origins of chaos theory were introduced by Henri Poincaré in 1908, who attempted to study an unsolved problem of Newtonian Laplacian celestial mechanics (the three-body problem). During this research, Poincaré realized that infinitely complex behavior may exist in nonlinear systems. Chaos theory, firstly discussed by MIT meteorologist Edward Lorenz, who simulated weather patterns on computers in the 1960 \cite{18}. In recent years, deterministic chaos has been seen as a model in electronic circuits, laser technology, cardiology, organizations, financial markets, urban communities, and climate.\\Chaos is a concept often used for a nonlinear dynamic. Chaos theory is a mathematical tool that extracts beautiful structures from chaos. The origins of chaos theory were introduced by Henri Poincaré in 1908, who attempted to study an unsolved problem of Newtonian Laplacian celestial mechanics (the three-body problem). During this research, Poincaré realized that infinitely complex behavior may exist in nonlinear systems. Chaos theory, firstly discussed by MIT meteorologist Edward Lorenz, who simulated weather patterns on computers in the 1960 \cite{18}. In recent years, deterministic chaos has been seen as a model in electronic circuits, laser technology, cardiology, organizations, financial markets, urban communities, and climate.\\Chaos is a concept often used for a nonlinear dynamic. Chaos theory is a mathematical tool that extracts beautiful structures from chaos. The origins of chaos theory were introduced by Henri Poincaré in 1908, who attempted to study an unsolved problem of Newtonian Laplacian celestial mechanics (the three-body problem). During this research, Poincaré realized that infinitely complex behavior may exist in nonlinear systems. Chaos theory, firstly discussed by MIT meteorologist Edward Lorenz, who simulated weather patterns on computers in the 1960 \cite{18}. In recent years, deterministic chaos has been seen as a model in electronic circuits, laser technology, cardiology, organizations, financial markets, urban communities, and climate.\\Chaos is a concept often used for a nonlinear dynamic. Chaos theory is a mathematical tool that extracts beautiful structures from chaos. The origins of chaos theory were introduced by Henri Poincaré in 1908, who attempted to study an unsolved problem of Newtonian Laplacian celestial mechanics (the three-body problem). During this research, Poincaré realized that infinitely complex behavior may exist in nonlinear systems. Chaos theory, firstly discussed by MIT meteorologist Edward Lorenz, who simulated weather patterns on computers in the 1960 \cite{18}. In recent years, deterministic chaos has been seen as a model in electronic circuits, laser technology, cardiology, organizations, financial markets, urban communities, and climate.\\

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