Dynamics and analogue circuit of a class of new Hénon maps and its application in the welded beam optimal design

At present, design and applications of discrete chaotic systems aroused much interests of scholars. A practical way to design new chaotic systems is based on existing classical systems. In this paper, based on the existing Hénon map, a class of new Hénon maps are proposed and investigated. Furthermore, the dynamic characteristics of a chosen map are analyzed by numerical simulations including phase diagrams, bifurcation diagrams and Lyapunov exponents. It shows that the system has rich dynamical behaviors. An analogue circuit of the new system is designed and its real hardware circuit is realized. The experiment demonstrates the succuss of the design. Finally, an application in the design of welded beams is carried out using the golden Jackal optimization algorithm which is improved based on the randomness and ergodicity of the generated chaos. The potential practical application based on the proposed system in the engineering field is demonstrated.