What is the simplest dissipative chaotic jerk equation which is parity invariant?
✍ Scribed by J.-M. Malasoma
- Book ID
- 104337980
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 404 KB
- Volume
- 264
- Category
- Article
- ISSN
- 0375-9601
No coin nor oath required. For personal study only.
✦ Synopsis
We investigate the chaotic dynamics of an autonomous scalar third-order differential equation. This system seems to be the algebraically simplest and previously unknown example of a dissipative chaotic jerky flow which is parity invariant. It displays chaotic behaviours in two distinct ranges of its control parameter. Deterministic chaos is principally observed from a symmetric limit cycle which after a symmetry-breaking bifurcation gives rise to two cascades of flip bifurcation. Then two coexisting asymmetric chaotic attractors are observed, and after a symmetry-restoring crisis a symmetric chaotic attractor is created. Chaotic attractors also coexist in another very narrow range of control parameter as results of two period doubling cascades of bifurcation from a pair of mutually symmetric coexisting limit cycles.