Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: This work presents a simplified and improved method of computing asymptotic unfoldings that can be used in any normal form style using normal (and hypernormal) form methods.
19 citations
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TL;DR: In this article, an asymptotic approach to gated ionic models of single-cell cardiac excitability is proposed, which allows a dynamical variable may change its character from fast to slow within a single solution.
19 citations
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TL;DR: The Euler-Poincare equations describing geodesics on Lie groups with invariant metrics fall into the class of quasihomogeneous systems with homogeneous quadratic right-hand members as mentioned in this paper.
Abstract: An example is a system with homogeneous quadratic right-hand members: in it, gl = ... = gn = i. Among others, the Euler-Poincare equations describing geodesics on Lie groups with invariant metrics fall into this class. A popular example from dynamics is Kirchoff's problem on the motion of a rigid body in an unbounded volume of an ideal liquid. Quasihomogeneous systems are also exemplified by the equations of the problem of many gravitating bodies and by the Euler-Poisson equations describing the rotation of a heavy rigid body about a fixed point. These remarks show that it is expedient to consider quasihomogeneous systems from the viewpoint of applications.
19 citations
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TL;DR: In this paper, the authors investigated the global asymptotic behavior of solutions of the system of difference equations where the parameters A and B are in (0, ∞) and the initial conditions x 0 and y 0 are arbitrary nonnegative numbers.
Abstract: Dedicated to Allan Peterson on the Occasion of His 60th Birthday. We investigate the global asymptotic behavior of solutions of the system of difference equations where the parameters A and B are in (0, ∞) and the initial conditions x 0 and y 0 are arbitrary nonnegative numbers. We show that the stable manifold of this system separates the positive quadrant into the basins of attraction of two types of asymptotic behavior.
19 citations