By Guanrong Chen, Xinghuo Yu

Chaos keep an eye on refers to purposefully manipulating chaotic dynamical behaviors of a few complicated nonlinear structures. There exists no comparable keep watch over theory-oriented booklet in the market that's dedicated to the topic of chaos keep watch over, written through keep an eye on engineers for keep watch over engineers. World-renowned best specialists within the box offer their state of the art survey in regards to the broad study that has been performed over the past few years during this topic. the hot expertise of chaos keep watch over has significant impression on novel engineering functions corresponding to telecommunications, strength platforms, liquid blending, net know-how, high-performance circuits and units, organic structures modeling just like the mind and the guts, and determination making. The booklet is not just geared toward lively researchers within the box of chaos keep watch over related to keep an eye on and structures engineers, theoretical and experimental physicists, and utilized mathematicians, but in addition at a common viewers in similar fields.

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**Example text**

28 G. Chen et al. Using the “controllability via stabilizability” method of Russell [21] for timereversible distributed parameter systems, one can prove that the exact controllability problem is solvable if T > 0 is suﬃciently large. ) So the linear feedback boundary condition (8) is nice and useful. However, in the design of many servomechanisms, stabilizability or controllability are not issues of any concern. What is really of concern is the safe or robust operation of the servomechanism. One such example is the classical van der Pol equation x ¨ − (α − β x˙ 2 )x˙ + kx = 0; α, β > 0, (11) where x = x(t) is proportional to the electric current at time t on a circuit equipped with a van der Pol device.

Maza, D. (2000) The control of chaos: theory and applications. Phys. , 329:103–197 63. , Kostelich, E. , Arecchi, F. T. (1997) Adaptive targeting of chaos. Phys. Rev. E,. 55:R4845-R4848 64. , Pethel, S. (2002) Control of long periodic orbits and and arbitrary trajectories in chaotic systems using dynamic limiting. Chaos 12(1):1–7 65. Corron, N. , Pethel, S. , Hopper, B. A. (2000) Controlling chaos with simple limiters. Phy. Rev. , 84:3835–3838 66. Wiggins, S. (1992) Chaotic Transport in Dynamical Systems.

P. Tian and X. Yu Let x(t) ∈ i∈Q Xi be a continuous piecewise C 1 function on the time interval [0, ∞). We say x(t) is a trajectory of (1) (or, of (3) for the piecewise linear case) if derivative x(t) ˙ is well defined for any t ≥ 0, the equation (1) (or (3) respectively) holds for all q with x(t) ∈ Xq . Let s = {s1 , s2 , · · · , si , · · · } be the sequence of discrete states associated with the continuous trajectory x(t). The sequence s actually defines the so-call symbolic dynamics of the system.