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(Nowa strona: Hénon attractor for ''a'' = 1.4 and ''b'' = 0.3 The '''Hénon map''' is a discrete-time dynamical system. It is one of the most studied exa...) |
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The map depends on two parameters, ''a'' and ''b'', which for the '''canonical Hénon map''' have values of ''a'' = 1.4 and ''b'' = 0.3. For the canonical values the Hénon map is chaotic. For other values of ''a'' and ''b'' the map may be chaotic, intermittent, or converge to a periodic orbit. An overview of the type of behavior of the map at different parameter values may be obtained from its [[orbit diagram]]. | The map depends on two parameters, ''a'' and ''b'', which for the '''canonical Hénon map''' have values of ''a'' = 1.4 and ''b'' = 0.3. For the canonical values the Hénon map is chaotic. For other values of ''a'' and ''b'' the map may be chaotic, intermittent, or converge to a periodic orbit. An overview of the type of behavior of the map at different parameter values may be obtained from its [[orbit diagram]]. | ||
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Wersja z 09:11, 24 mar 2010
The Hénon map is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. The Hénon map takes a point (xn, yn) in the plane and maps it to a new point
\[\begin{align} x_{n+1} &= y_n+1-a x_n^2,\\ y_{n+1} &= b x_n. \end{align}\]
The map depends on two parameters, a and b, which for the canonical Hénon map have values of a = 1.4 and b = 0.3. For the canonical values the Hénon map is chaotic. For other values of a and b the map may be chaotic, intermittent, or converge to a periodic orbit. An overview of the type of behavior of the map at different parameter values may be obtained from its orbit diagram. sddd