Eur. Phys. J. Spec. Top. (2022) 231: 2467-2476
https://doi.org/10.1140/epjs/s11734-022-00487-9

Regular Article

Dynamics of a fractional-order Colpitts oscillator and its FPGA implementation

¹ School of Physics and Electronics, Central South University, 410083, Changsha, China
² School of Mechanical and Electrical Engineering, Guizhou Normal University, 550025, Guiyang, China

^d heshaobo@csu.edu.cn

Received: 29 November 2021
Accepted: 17 February 2022
Published online: 16 April 2022

Abstract

In this paper, a fractional-order Colpitts oscillator is investigated by employing multi-step fractional differential transform method as well as implemented on Field Programmable Gate Array (FPGA). Dynamic characteristics of the fractional-order system are analyzed using bifurcation diagrams, Lyapunov exponents, phase diagrams, and FuzzyEn complexity. Comparisons between the fractional-order Colpitts oscillator and the corresponding integer-order system show that the former has better dynamic properties. Phase diagrams implemented on FPGA are consistent well with simulation results. The main superiority of FPGA implementation is its flexibility in practical applications. It is easy to configure the values of derivative orders, step size, and system parameters in real time without changing hardware architecture, which lays a foundation for the application of the fractional-order Colpitts system.