Chaos and hyperchaos in a gyrotron

Abstract

We study oscillation in a gyrotron with allowance for reflections from an output horn. Regions with different system behaviors, such as stationary oscillation, self-modulation, and complexdynamics regimes are found in the parameter plane. The scenarios of appearance of chaotic oscillations are considered. It is shown that they can emerge via either a sequence of perioddoubling bifurcations or destruction of quasiperiodic motion. For chaotic attractors, Lyapunov exponents are calculated and their dimensions are estimated on the basis of the Kaplan-Yorke formula. The dimension values turn out to be anomalously large, which is stipulated by the presence of a large number of high-Q eigenmodes in the gyrotron cavity due to operation near the cutoff frequency of an electrodynamic system.

Archives of Control Sciences

“…For a 4-D autonomous hyperchaotic system, there are two positive Lyapunov exponents, one zero and one negative Lyapunov exponent [1]. Hyperchaotic systems are applied in several engineering areas such as lasers [2,3], power systems [4,5], oscillators [6][7][8][9][10], neural networks [11][12][13][14], cryptosystems [15][16][17][18], neurons [19,20], memristors [21][22][23], etc. Chaotic dynamical systems have been recently classified into two categories viz.…”