Download e-book for kindle: Analysis and Control of Complex Dynamical Systems: Robust by Kazuyuki Aihara, Jun-ichi Imura, Tetsushi Ueta

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 record on theoretical breakthroughs on keep watch over of advanced dynamical structures built by way of collaborative researchers within the fields of dynamical platforms thought and regulate concept. besides, its uncomplicated standpoint is of 3 varieties 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 regulate of complicated Dynamical Systems deals a precious source for mathematicians, physicists, and biophysicists, in addition to for researchers in nonlinear technological know-how and regulate engineering, letting them increase a greater basic figuring out of the research and keep watch over synthesis of such advanced systems.

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

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From the open circle, our method can obtain a local optimal parameter value. From the closed circle, our method also reaches a local optimal parameter value: the farthest point from the bifurcations denoted by the solid curves. To achieve a global search, we use the third parameter λ3 . 2b shows the results when changing the value of parameter λ3 . 1. From this point, we can find the optimal parameter values denoted by the star. 3. 0 λ2 Fig. 2 Results for Duffing’s equations. Solid curves indicate the bifurcation sets of the fixed point corresponding to the non-resonant state.

IEEE Trans. Circuits Syst. CAS-31(3), 248–260 (1984) 22. : An algorithm tracing out the tangent bifurcation curves and its application to Duffing’s equation, IEICE Trans. Fundam. 1 Introduction Discrete-time dynamical systems [2] are widely used for mathematical modeling of various systems. In many cases, desired behavior in nonlinear discrete-time dynamical systems corresponds to stable fixed and periodic points. The values of system parameters can be determined through bifurcation analysis [9, 10, 15] in advance so that desired behavior is produced in a steady state.

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.

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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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