Dynamics, circuit design and fractional-order form of a modified rucklidge chaotic system

Sambas, A. and Vaidyanathan, S. and Mamat, M. and Sanjaya WS, M. and Yuningsih, S.H. and Zakaria, K. and Subiyanto, . (2018) Dynamics, circuit design and fractional-order form of a modified rucklidge chaotic system. In: International Conference on Computation in Science and Engineering, ICCSE 2017, 10-12 Jul 2017, Bandung, Indonesia.

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Abstract

Rucklidge chaotic system is a nonlinear mechanical model of a double convection process. In this paper, we modify the dynamics of a Rucklidge chaotic system by adding a nonlinear term and derive a new chaotic system. The nonlinear dynamics of the proposed chaotic system is described through numerical simulations which include the stability analysis of equilibrium points, phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and a Poincare map. For specific values of the parameters, the proposed system displays periodic and chaotic behaviour. In addition, a new circuit implementation of the modified Rucklidge chaotic system is reported and examined in MultiSIM. A good qualitative agreement is shown between the simulations and the MultiSIM results. Furthermore, the fractional-order form of the modified Rucklidge chaotic system is numerically studied. By tuning the commensurate fractional order, the new chaotic system displays chaotic and periodic attractors, respectively.

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