Mirroring and nonlinear perturbation of a circuit's system with multiple attractors

• Published in: Mathematical modelling and analysis Vol. 29; no. 4; pp. 731 - 752
• Main Author: Doungmo Goufo, Emile Franc
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 29.11.2024
• Subjects: Analysis; Attractors (mathematics); Boundary value problems; Circuit diagrams; circuit implementation; Dynamical systems; electric circuit diagram; Error analysis; Field programmable gate arrays; limit cycles; mirror symmetry conversion process; Numerical analysis; Numerical methods; perturbation; Simulation methods; Strange attractors; Symmetry; electric circuit diagram; mirror symmetry conversion process; circuit implementation; perturbation; limit cycles
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2024.21033

We infix the duality-symmetric and the mirror symmetry conversion processes into a dynamical system representing an electric circuit diagram with three input (or output) as shown in Figure 2. Hence, a new non-linear variable order initial value problem is obtained and solved using the Haar wavelet numerical method (HWNM). Error, stability and entropy analyzes show the reliability of the method. Numerical simulations are then implemented and show for the new system, existence of various attractors’ types (point attractors (PAs), limit cycles, strange attractors (SAs), double attractor (DA), coexisting attractors (CoAs)) with their mirror reflections. Both are in a symmetrical structure in which they face each other, separated by a changing symmetry line and exhibiting similar properties. The circuit implementation using a Field Programmable Gate Array (FPGA) is performed and concur with the expected results.