Modelling, bifurcation analysis, circuit design and FPGA-based implementation of a new chaotic jerk system exhibiting Hopf bifurcations

It is well-known that chaotic systems have several applications in scientific modelling and engineering fields such as encryption, cryptosystems, secure communication, etc. This work proposes a three-dimensional mechanical chaotic system with jerk dynamics. A detailed bifurcation analysis is conducted for the proposed chaotic system. It is shown that the proposed chaotic system has two equilibrium points which exhibit Hopf bifurcations. It is also shown that the proposed chaotic system depicts multi-stability and co-existing chaotic attractors. Using MultiSim (Version 14), an electronic circuit is designed for the proposed mechanical chaotic system with jerk dynamics. As another engineering application, field programmable gate array (FPGA) design has been made for the proposed mechanical jerk chaotic system. Euler's finite-difference method is used for our FPGA design. A hardware implementation of the FPGA-based design is performed in this work and experimental results are given in detail.