By Guanrong Chen, Xinghuo Yu
Chaos keep watch over refers to purposefully manipulating chaotic dynamical behaviors of a few complicated nonlinear platforms. There exists no comparable keep an eye on theory-oriented booklet out there that's dedicated to the topic of chaos keep an eye on, written through keep an eye on engineers for keep watch over engineers. World-renowned top specialists within the box supply their state of the art survey in regards to the huge examine that has been performed over the past few years during this topic. the hot expertise of chaos regulate has significant impression on novel engineering purposes comparable to telecommunications, energy platforms, liquid blending, web expertise, high-performance circuits and units, organic platforms modeling just like the mind and the center, and choice making. The ebook isn't just aimed toward lively researchers within the box of chaos keep an eye on concerning keep watch over and structures engineers, theoretical and experimental physicists, and utilized mathematicians, but in addition at a basic viewers in comparable fields.
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Extra resources for Chaos Control: Theory and Applications
Atmos. , 20:130-141 2. , Yorke, J. A. (1990) Controlling chaos. Phys. Rev. , 64:1196–1199 3. , Dayawansa, W. (1992) Contolling chaotic dynamical systems. Physica D, 58(1002):165–192 4. , Smale, S. (1974) Diﬀerential Equations, Dynamical Systems and Linear Algebra. New York: Academic Press 5. , (1998) Optimal targeting of chaos. Phys. Lett. A, 245(5):399–406 6. , Yorke, J. A. (1992) Using chaos to direct orbits to targets in systems describable by a one-dimensional map. Phys. Rev. A, 45:4165-4168 7.
When η > 1, the results are similar. See . G. Chen et al. 36 (2) With the nonlinear boundary condition (16), we can only establish that u and v are chaotic. , the gradient of w, are also chaotic by a natural topological conjugacy, see [3, Section 5]. However, w itself is not chaotic because w is the time integral of wt , which smooths out the oscillatory behavior of wt . In order to have chaotic vibration of w, one must use a diﬀerentiated boundary condition; see [4, Section 6]. This is actually an analog of (13).
1 Introduction The onset of chaotic phenomena in systems governed by nonlinear partial differential equations (PDEs) has fascinated scientists and mathematicians for many centuries. The most famous case in point is the Navier–Stokes equations and related models in ﬂuid dynamics, where the occurrence of turbulence in ﬂuids is well accepted as a chaotic phenomenon. Yet despite the diligence of numerous of the most brilliant minds of mankind, and the huge amount of new knowledge gained through the vastly improved computational and experimental methods and facilities, at present we still have not been able to rigorously prove that turbulence is indeed chaotic in a certain universal mathematical sense.