Dynamics of a two-frequency parametrically driven duffing oscillator

Summary We investigate the transition from two-frequency quasiperiodicity to chaotic behavior in a model for a quasiperiodically driven magnetoelastic ribbon. The model system is a two-frequency parametrically driven Duffing oscillator. As a driving parameter is increased, the route to chaos takes place in four distinct stages. The first stage is a torus-doubling bifurcation. The second stage is a transition from the doubled torus to a strange nonchaotic attractor. The third stage is a transition from the strange nonchaotic attractor to a geometrically similar chaotic attractor. The final stage is a hard transition to a much larger chaotic attractor. This latter transition arises as the result of acrisis, the characterization of which is one of our primary concerns. Numerical evidence is given to indicate that the crisis arises from the collision of the chaotic attractor with the stable manifold of a saddle torus. Intermittent bursting behavior is present after the crisis with the mean time between bursts scaling as a power law in the distance from the critical control parameter; τ ∼ (A-A_c)^-α. The critical exponent is computed numerically, yielding the value α=1.03±0.01. Theoretical justification is given for the computed critical exponent. Finally, a Melnikov analysis is performed, yielding an expression for transverse crossings of the stable and unstable manifolds of the crisis-initiating saddle torus.     

Chaotic resonance: A simulation

Stochastic resonance is a statistical phenomenon that has been observed in periodically modulated, noise-driven, bistable systems. The characteristic signatures of the effect include an increase in the signal-to-noise of the output as noise is added to the system, and exponentially decreasing peaks in the probability density as a function of residence times in one state. Presented are the results of a numerical simulation where these same signatures were observed by adding achaotic driving term instead of a white noise term. Although the probability distributions of the noise and chaos inputs were significantly different, the stochastic and chaotic resonances were equal within the experimental error.     

Microwave-assisted acylation of 7-amino-5-aryl-6-cyanopyrido[2,3-d]pyrimidines

A microwave-assisted method is described for monoacylating 7-amino-5-aryl-6-cyanopyrido[2,3-d]pyrimidines using excess acid chlorides in pyridine. A diacylated intermediate is effectively deacylated to the product amide by a macroporous-Tris resin. A small library of 17 amides was prepared to validate the method. The integration of commercial microwave technology into the ArQule chemistry platform is also discussed.     

Chaogates: morphing logic gates that exploit dynamical patterns

Chaotic systems can yield a wide variety of patterns. Here we use this feature to generate all possible fundamental logic gate functions. This forms the basis of the design of a dynamical computing device, a chaogate, that can be rapidly morphed to become any desired logic gate. Here we review the basic concepts underlying this and present an extension of the formalism to include asymmetric logic functions.     

Control and synchronization of chaos in high dimensional systems: Review of some recent results

Controlling chaos and synchronization of chaos have evolved for a number of years as essentially two separate areas of research. Only recently it has been realized that both subjects share a common root in control theory. In addition, as limitations of low dimensional chaotic systems in modeling real world phenomena become increasingly apparent, investigations into the control and synchronization of high dimensional chaotic systems are beginning to attract more interest. We review some recent advances in control and synchronization of chaos in high dimensional systems. Efforts will be made to stress the common origins of the two subjects. (c) 1997 American Institute of Physics.