Criteria of uniqueness of limit cycle in a resonant-tunneling dynamic system

Abstract

The article addresses the criteria of uniqueness of limit cycle of a dynamic system dx/dt = y - P(x), dy/dt = ax + by + c. Criteria previously obtained for a system with P(x)=P3(x)= a1x+a2x2+a3x3 are generalized to a system with function P(x), having the form of the current–voltage characteristic of a resonant-tunneling diode. This generalization is useful because resonant-tunneling diodes are promising devices for application in terahertz oscillators, but their characteristics differ significantly from the cubic trinomial P3(x). The obtained criteria can be represented in a program language of any computer mathematics system, e.g., “Mathematica”.