Structural Stability in 4-Dimensional Canards

Structural Stability and Hyperbolicity Violation in High-Dimensional Dynamical Systems

This report investigates the dynamical stability conjectures of Palis and Smale, and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical system is increased, it is observed that the number of positive Lyapunov exponents increases monotonically, the Lyapunov exponents tend towards continuous ch...

Structural stability in the 4-zinc human insulin hexamer.

X-ray studies on human insulins prepared by semisynthetic and biosynthetic methods have recently been undertaken. Human insulin differs from porcine insulin only at the COOH terminus of the B-chain. The present study reports the crystal structure of 4-zinc human insulin, which is used clinically as a slow-acting preparation. The structure has been refined, using 1.85-A resolution data, to a res...

Comment on "Structural stability of complex hydrides: LiBH(4) revisited".

Numerical Computation of Canards

Singularly perturbed systems of ordinary differential equations arise in many biological, physical and chemical systems. We present an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that were numerically computed using continuat...

Feedback control of canards.

We present a control mechanism for tuning a fast-slow dynamical system undergoing a supercritical Hopf bifurcation to be in the canard regime, the tiny parameter window between small and large periodic behavior. Our control strategy uses continuous feedback control via a slow control variable to cause the system to drift on average toward canard orbits. We apply this to tune the FitzHugh-Nagumo...