Name
Abstract | ||
|---|---|---|
How fluctuations can be eliminated or attenuated is a matter of general interest in the study of steadily-forced dissipative nonlinear dynamical systems. Here, we extend previous work on "nonlinear quenching" [Hide, 1997] by investigating the phenomenon in systems governed by the novel autonomous set of nonlinear ordinary differential equations (ODE's) x = ay - ax, y = -xzq + bx - y and z = xyq - cz (where (x, y, z) are time (t)-dependent dimensionless variables and x = dx/dt, etc.) in representative cases when q, the "quenching function", satisfies q = 1 - e + ey with 0 less than or equal to e less than or equal to 1. Control parameter space based on a, b and c can be divided into two "regions", an S-region where the persistent solutions that remain after initial transients have died away are steady, and an F-region where persistent solutions fluctuate indefinitely. The "Hopf boundary" between the two regions is located where b = b(H) (a, c; e) (say), with the much studied point (a, b, c) = (10, 28, 8/3), where the persistent "Lorenzian" chaos that arises in the case when e = 0 was first found lying close to b = b(H) (a, c; 0). As e increases from zero the S-region expands in total "volume" at the expense of F-region, which disappears altogether when e = 1 leaving persistent solutions that are steady throughout the entire parameter space. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1142/S0218127404010904 | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS |
Keywords | DocType | Volume |
nonlinear quenching, chaos, nonlinear circuits | Journal | 14 |
Issue | ISSN | Citations |
8 | 0218-1274 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Raymond Hide | 1 | 0 | 1.01 |
| Patrick E. Mcsharry | 2 | 133 | 12.66 |
| Christopher C. Finlay | 3 | 0 | 0.34 |
| Guy D. Peskett | 4 | 0 | 0.34 |