Get Analysis and Control of Complex Dynamical Systems: Robust PDF

By Kazuyuki Aihara, Jun-ichi Imura, Tetsushi Ueta

ISBN-10: 4431550127

ISBN-13: 9784431550129

ISBN-10: 4431550135

ISBN-13: 9784431550136

This e-book is the 1st to file on theoretical breakthroughs on regulate of complicated dynamical platforms constructed by means of collaborative researchers within the fields of dynamical structures concept and regulate conception. in addition, its simple perspective is of 3 different types of complexity: bifurcation phenomena topic to version uncertainty, advanced habit together with periodic/quasi-periodic orbits in addition to chaotic orbits, and community complexity rising from dynamical interactions among subsystems. Analysis and keep an eye on of complicated Dynamical Systems deals a worthy source for mathematicians, physicists, and biophysicists, in addition to for researchers in nonlinear technology and keep watch over engineering, permitting them to advance a greater primary figuring out of the research and keep an eye on synthesis of such complicated systems.

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Extra resources for Analysis and Control of Complex Dynamical Systems: Robust Bifurcation, Dynamic Attractors, and Network Complexity

Example text

We use this normal vector to obtain the optimal parameter values. The procedure is summarized as follows: 1. Set the initial parameter value at which a target solution is stable. 2. 8), find the closet-bifurcation point [10] by searching several directions. To find a bifurcation point, we use the method described in [18]. 3. Change the parameter values in the opposite direction of the closet-bifurcation obtained in Step 2. 4. Repeat Step 2 and Step 3. 3 Results Here, we show the results of our method on discrete-time and continuous-time systems.

In the analysis, given an uncertain system described by a model set, we obtain an outer approximation of all the possible bifurcation points. Acknowledgments The authors gratefully acknowledge Takayuki Arai, Masayasu Suzuki, and Takayuki Ishizaki for their comments and fruitful discussion on this research. References 1. : Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. CRC Press, Boca Raton (1998) 2. : Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Springer, New York (2003) 3.

J. Math. Biol. 40(6), 525–540 (2000) 20. : Universal behavior in a generalized model of contagion. Phys. Rev. Lett. 92(21), 218701 (2004) 21. : Epidemic dynamics on an adaptive network. Phys. Rev. Lett. 96(20), 208701 (2006) 22. : Backward bifurcation of an epidemic model with treatment. Math. BioSci. 201(1–2), 58–71 (2006) 23. : Robust and Optimal Control. Prentice Hall, Upper Saddle River (1996) 24. : Multivariable Feedback Control: Analysis and Design, 2nd edn. Wiley-Interscience, New York (2005) 25.

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Analysis and Control of Complex Dynamical Systems: Robust Bifurcation, Dynamic Attractors, and Network Complexity by Kazuyuki Aihara, Jun-ichi Imura, Tetsushi Ueta


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