Access the full text.
Sign up today, get DeepDyve free for 14 days.
M. Klamkin, D. Newman (1971)
Cyclic Pursuit or “the Three Bugs Problem”American Mathematical Monthly, 78
F. Brauer, V. Arnold, R. Cook (1973)
Ordinary Differential Equations
F. Behroozi, R. Gagnon (1981)
Perimeter expansion in the n‐bug system and its relationship to stabilityJournal of Mathematical Physics, 22
B. Kuo (1962)
Automatic Control Systems
In a companion paper [5] we resolved the question of whether cyclic pursuits can exhibit ‘non-mutual’ captures. Although, as we showed, non-mutual captures can occur, the set of initial conditions which lead to them has Lebesgue measure zero. Thus, generically, cyclic pursuits collapse into a mutual capture. In this paper we consider whether the pursuit configuration can asymptotically approach a regular one for a non-trivial set of initial conditions. More precisely, we study the stability of regular geometries of cyclic pursuit. We show that in all dimensions the only stable regular n-bug shapes are the regular two dimensional n-gons, n≥7, in which each vertex chases its neighboring vertex in some fixed orientation. We also analize the three bug cyclic pursuit in detail, proving that, except for the equilateral initial position, the triangle formed is asymptotically degenerate with the minimum interior angle tending to zero while the vertex at which the minimum is located rotates among the vertices infinitely often.
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: Oct 19, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.