Based on insight obtained from a newly developed cochlea model, we argue that noise-driven limit cycles are the basic ingredient in the mammalian cochlea hearing process. For insect audition, we provide evidence in favor of the persistence of this principle. We emphasize the role of bifurcations for the emergence of broad-range sound perception, both in the frequency and amplitude domain, and i...

The existing disk instability model for dwarf nova eruptions is reviewed, in the light of recent progress in the understanding of angular momentum transport in accretion disks. It is proposed that the standard lower branch in the “S-curve” in the effective temperature-surface density plane may not exist. Rather, angular momentum transport may be suppressed in quiescence as a result of cooling. ...

Seth L. Lacy Air Force Research Lab, Space Vehicles Kirtland AFB NM 87117 [email protected] Dennis S. Bernstein Aerospace Engineering, University of Michigan Ann Arbor MI 48109 [email protected] Abstract Limit cycle oscillations occur in a wide range of electrical, mechanical, and aerospace applications. In this paper we present a method for constructing system models that are able to r...

We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic polynomial differential systems we prove that at most three limit cycles can bifurcate from the degenerate center. As far as we know this is the first time that a com...

We construct a Gause-type predator-prey model with concave prey isocline and (at least) two limit cycles. This serves as a counter-example to the global stability criterion of Hsu [Math. Biosci. 39:1-10 (1978)].