Parameter identification for Van Der Pol–Duffing oscillator by a novel artificial bee colony algorithm with differential evolution operators

• Identification of Van Der Pol–Duffing oscillators.
• Contraction techniques for searching area.
• Re-initialization strategy on number theory.
• A novel ABC with differential evolution operators.

This paper is concerned with the uncertain parameters’ identification of Van Der Pol–Duffing oscillators (VDPD) through a non-Lyapunov way with ABC and ABCDEO respectively by converting the problem into a multiple modal non-negative functions’ minimization, which is of vital significance and attracts increasing interests in various research fields. Firstly, a novel artificial bee colony (ABC) algorithm with differential evolution operators (ABCDEO) is introduced to accelerate ABC due to the slow nature of the collective intelligence of honey bee swarms, by doing differential evolution operators to the employed bees colony in a certain probability, a special region contraction rules, and swarm re-initialization strategy based on number-theory nets. Secondly, the unknown parameters of VDPD for three main physical states, the cases with noise, and a comprehensive set of twelve complex benchmark functions including a wide range of dimensions, are employed for experimental verification. Experimental results confirm that the ABCDEO is a successful method in VDPD’s parameters’ identification.