Uniform stability of displacement coupled second-order equations.
Uniqueness of limit cycles bounded by two invariant parabolas
In this paper we consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas.
Universality and scaling in networks of period-doubling maps with a pacemaker.
Using density matrices in classical dynamical systems
Using normal mode analysis in teaching mathematical modeling to biology students
Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators to model the fluctuations of molecular structures around the equilibrium state. I present many learning...