Author | Parker, Thomas S. author |
---|---|
Title | Practical Numerical Algorithms for Chaotic Systems [electronic resource] / by Thomas S. Parker, Leon O. Chua |
Imprint | New York, NY : Springer New York, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3486-9 |
Descript | XIV, 348 p. online resource |
1 Steady-State Solutions -- 1.1 Systems -- 1.2 Limit sets -- 1.3 Summary -- 2 Poincarรฉ Maps -- 2.1 Definitions -- 2.2 Limit Sets -- 2.3 Higher-order Poincarรฉ maps -- 2.4 Algorithms -- 2.5 Summary -- 3 Stability -- 3.1 Eigenvalues -- 3.2 Characteristic multipliers -- 3.3 Lyapunov exponents -- 3.4 Algorithms -- 3.5 Summary -- 4 Integration -- 4.1 Types -- 4.2 Integration error -- 4.3 Stiff equations -- 4.4 Practical considerations -- 4.5 Summary -- 5 Locating Limit Sets -- 5.1 Introduction -- 5.2 Equilibrium points -- 5.3 Fixed points -- 5.4 Closed orbits -- 5.5 Periodic solutions -- 5.6 Two-periodic solutions -- 5.7 Chaotic solutions -- 5.8 Summary -- 6 Manifolds -- 6.1 Definitions and theory -- 6.2 Algorithms -- 6.3 Summary -- 7 Dimension -- 7.1 Dimension -- 7.2 Reconstruction -- 7.3 Summary -- 8 Bifurcation Diagrams -- 8.1 Definitions -- 8.2 Algorithms -- 8.3 Summary -- 9 Programming -- 9.1 The user interface -- 9.2 Languages -- 9.3 Library definitions -- 10 Phase Portraits -- 10.1 Trajectories -- 10.2 Limit sets -- 10.3 Basins -- 10.4 Programming tips -- 10.5 Summary -- A The Newton-Raphson Algorithm -- B The Variational Equation -- C Differential Topology -- C.1 Differential topology -- C.2 Structural stability -- D The Poincarรฉ Map -- E One Lyapunov Exponent Vanishes -- F Cantor Sets -- G List of Symbols