Simple Driven Maps As Sensitive Devices.pdf

a r X i v : n l i n / 0 0 0 5 0 0 3 v 1 [ n l i n .C D ] 2 9 A p r 2 0 0 0 Simple Driven Maps As Sensitive Devices Changsong Zhou1 and C.-H. Lai1,2 1Department of Computational Science and 2Department of Physics National University of Singapore, Singapore 119260 Abstract Sensitive dependence of nonlinear systems on initial conditions or parameters can be useful in applications. We propose in this paper that bubbling behavior in simple driven symmetrical maps may be used as a working principle of sensitive devices. The system is stable when there is no input and displays bursting behavior when there is small input. The symmetrical property of the bursting pattern is very sensitive to the bias of the noisy inputs, which makes the system promising for detecting weak signals among noisy environment. PACS number(s): 05.45.+b; 1 A common property of many nonlinear systems is their sensitive dependence on initial conditions or parameters. This effect can be useful in applications. For example, the sensitiv- ity of a chaotic system can be used to control its state to unstable periodic orbits embedded in it [1], in targeting the state of the system to desired points in the state space[2], to control the system to follow a desired goal dynamics in order to synchronize with another system[3] or to allow a message being encoded in a chaotic series for the purpose of secure communication[4], only by small modifications of the parameters or state of the chaotic system. The capability of achieving quite different behavior by applying only small perturbations improves greatly the flexibility of a system to be used in various applications. By definition, sensitivity is referred to as the growth of small perturbations to the system. So, naively, sensitivity of nonlinear systems can be used to design sensor devices. Many systems possess a period-doubling bifurcation when some parameter is varied. Near the onset of a period-doubling bifurcation, any dynamical system can be used