Articles written in Pramana – Journal of Physics
Volume 90 Issue 5 May 2018 Article ID 0063 Research Article
The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil’nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify thefeasibility of this new grid multiwing chaotic system.
Volume 91 Issue 6 December 2018 Article ID 0082 Research Article
In this paper, two kinds of novel non-ideal voltage-controlled multi-piecewise cubic nonlinearity memristors and their mathematical models are presented. By adding the memristor to the circuit of a three dimensional jerk system, a novel memristive multiscroll hyperchaotic jerk system is established without introducing any other ordinary nonlinear functions, from which $2N + 2$-scroll and $2M + 1$-scroll hyperchaotic attractors are achieved. It is exciting to note that this new memristive system can produce the extreme multistability phenomenonof coexisting infinitely multiple attractors. Furthermore, the dynamical behaviours of the proposed system are analysed by phase portraits, equilibrium points, Lyapunov exponents and bifurcation diagrams. The results indicate that the system exhibits hyperchaotic, chaotic and periodic dynamics. Especially, the phenomenon of transient chaoscan also be found in this memristive multiscroll system. Additionally, the MULTISIM circuit simulations and the hardware experimental results are performed to verify numerical simulations.
Volume 93 | Issue 6
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