| Budget Amount *help |
¥17,160,000 (Direct Cost: ¥13,200,000、Indirect Cost: ¥3,960,000)
Fiscal Year 2012: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2011: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2010: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2009: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
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| Research Abstract |
A great improvement of the Conley-Morse graph method, a computer-assisted method that analyzes global dynamics and bifurcations by combining a topological method and validated numerical computation has been done by developing a computer-algorithm for generating so-called clutching graphs which describe relation between Conley-Morse graphs on adjacent parameter domains. Another improvement is a method of non-uniform grid decomposition of the phase space in order to substantially decrease computational cost of the Conley-Morse graph method.A new approach to the bifurcation theory of dynamical systems from topological-computation theory viewpoint has been proposed which captures bifurcation of dynamics from changes of the corresponding Conley-Morse graphs. From this viewpoint, we have obtained a new mathematical framework for the crisis bifurcation.Moreover, we have studied the global dynamics of a Coupled Map Lattice system and a Coupled Oscillator system by using the Conley-Morse graph method, and have obtained the creation and bifurcations of some global dynamics such as unstable invariant tori and their connecting orbits.
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