D. R. J. Chillingworth, Differential Topology with a View to Applications. London: Pitman, 1976. Home/Search Document Not in Database Summary Related Articles Check |
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Discovering Coherent Structures in Nonlinear Spatial Systems - Crutchfield (1992) (3 citations) (Correct)
....cycle, and chaotic attractors. Decomposing a given system s behavior into this list of objects, the attractor basin portrait, yields a picture of the global organization of its solutions. Important information is extracted in this way without recourse to exact solution of the equations of motion. [1] This geometric view when coupled with the realization that apparent unpredictability can be generated by simple, but nonlinear dynamical systems has lead in recent years to the development of nonlinear modeling . 2] This endeavor has many aspects, but speaking broadly the goal is to discover ....
....Previous investigations of CA patterns have focused on the global machine M t . 18, 19] In terms of dynamical systems theory, though, the global machine describes the entire attractor basin portrait: the collection of all invariant sets and transients, including attractors and separatrices. [1] In many cases, this description is seen to be prohibitively difficult to construct because, for example, M t grows too large with time. In fact, such complete global descriptions are rarely pursued in dynamical systems theory. Even for elementary CA, there are many cases in which the size of M t ....
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D. R. J. Chillingworth, Differential Topology with a View to Applications. London: Pitman, 1976.
A Converse Theorem for Exponential Stability using.. - Pettersson, Lennartson (Correct)
....The remaining points are placed along the curve T x t in the same manner, see Figure 2a. The final point x i 2 T x t is placed at the origin (denoted by xm in Figure 2a) Since the closure of T x t is a compact space, which implies that every cover of T x t by open regions has a finite sub cover [2], there is only a finite number of intermediate points x i 2 T x t . The trajectories that evolve from x 0 2 T x t obviously satisfy the stability conditions if switchings from V i to V j occur at states B r ij (i) B r j (i) where i is either x i or x j , cf. above. Figure 2b illustrates a ....
D. Chillingworth. Differential Topology with a view to Applications. Pitman, 1976.
Dynamical System Prediction: a Lie algebraic approach for a .. - Moreau, Vandewalle (1993) (Correct)
....we call MLP in dynamics space . Finally, we will conclude. 1.1 Dynamical systems A dynamical system is a rule for the evolution over time of a set of variables. This set of variables is called the state of the system. Following the general differential geometric definition of dynamical systems [2], the state will be identified here with some point on a manifold M. We will consider here only those systems for which the state evolves according to some ordinary differential equation x(t) f(x(t) The function f is the vector field of the system and it associates to each point of the ....
D.R.J.Chillingworth, Differential topology with a view to applications., Pitman Publishing, London, 1977.
-16 17 -1 - Fig Dislocation (Correct)
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D. R. J. Chillingworth. Differential Topology with a View to Applications. Pitman, London, 1976.
ECA 18 Temporal Decay - Crutchfield, Hanson (Correct)
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D. R. J. Chillingworth. Differential Topology with a View to Applications. Pitman, London, 1976.
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