Zip and velcro bifurcations in competition models in ecology and economics

Abstract

During the last six years or so, a number of interesting papers discussed systems with line segments of equilibria, planes of equilibria, and with more general equilibrium configurations. This note draws attention to the fact that such equilibria were considered previously by Miklós Farkas , in papers published in . He called zip bifurcations those involving line segments of equilibria, and velcro bifurcations those involving planes of equilibria. We briefly describe prototypical situations involving zip and velcro bifurcations.

Special chaotic systems

“…Some of the papers investigate chaotic systems from the real-world [44][45][46][47][48][49][50][51]. Authors in [48] discuss a chaotic map of the process equation as a model for the development of cells.…”

“…The author in [50] describes two simple variants of the Nose-Hoover oscillator, the first of which satisfies the original goal exactly, and the second of which exhibits a hidden global chaotic attractor that fills all of its three-dimensional state space. The author in [45] states that during the last six years or so, several exciting papers have discussed systems with line segments of equilibria or planes of equilibria, and systems with more general configurations. It draws attention to the fact that such equilibria were considered previously by Miklos Farkas , in papers published in 1984-2005.…”