Grid Multiscroll Hyperchaotic Attractors Based on Colpitts Oscillator Mode with Controllable Grid Gradient and Scroll Numbers

 

Fei Yu^1,2, Chunhua Wang*¹, Haizhen He¹

 

¹ College of Information Science and Engineering, Hunan University, Changsha 410082, PR China. *wch1227164@sina.com.

² School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410004, PR China.

 

ABSTRACT

Through introducing two piecewise-linear triangular wave functions in a three-dimensional spiral chaotic Colpitts oscillator model, a four-dimensional grid multiscroll hyperchaotic system is constructed. Interestingly, by adjusting a build-in parameter in a variable of one triangle wave function, the control of the gradient of the multiscroll grid is achieved. Whereas by deploying the zero points of the two triangular wave functions to extend the saddle-focus equilibrium points with index-2 in phase space the scroll numbers do not only increase along with the number of turning points, but they can also generate arbitrary multiples of products. The basic dynamical behaviors of the proposed four-dimensional multiscroll hyperchaotic system are analyzed. Finally, the hardware experimental circuit is designed and the interrelated circuit implementation is realized. The experimental results are in agreement with both theoretical analyses and numerical simulations, which verify the feasibility of the design methods.

Keywords: Colpitts oscillator mode, triangle wave functions, hyperchaotic system, grid gradient, scroll numbers.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

References

[1] A. Ashraf and A. Abdulnasser, "On the design of chaos-based secure communication systems," Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 9, pp. 3721-3737, 2011.         [ Links ]

[2] J. L. Mata-Machuca et al., "Chaotic Systems Synchronization Via High Order Observer Design," Journal of Applied Research and Technology, vol. 9, no. 1, pp. 57-68, 2011.         [ Links ]

[3] C. Posadas-Castillo et al., "Experimental realization of binary signals transmission based on synchronized Lorenz circuits," Journal of Applied Research and Technology, vol. 2, no. 2, pp. 127-137, 2004.         [ Links ]

[4] G. Grassi et al., "Multi-wing hyperchaotic attractors from coupled Lorenz systems," Chaos, Solitons & Fractals, vol. 41, no. 1, pp. 284-291, 2009.         [ Links ]

[5] C. Zhang and S. Yu, "Generation of grid multi-scroll Chua's chaotic attractors with combination of hysteresis and step series," Acta Physica Sinica, vol. 58, no. 1, pp. 120-130, 2009.         [ Links ]

[6] R. N. Perez, "Measurement of Chua chaos and its applications," Journal of Applied Research and Technology, vol. 6, no. 1, pp. 45-53, 2008.         [ Links ]

[7] J. M. Muñoz-Pacheco and E. Tlelo-Cuautle, "Automatic synthesis of 2D-n-scrolls chaotic systems by behavioral modeling," Journal of Applied Research and Technology, vol. 7, no. 1, pp. 5-14, 2009.         [ Links ]

[8] J. Lü et al., "Design and analysis of multiscroll chaotic attractors from saturated function series," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 51, no. 12, pp. 2476-2490, 2004.         [ Links ]

[9] J. Lü et al., "Experimental verification of multidirectional multi-scroll chaotic attractors," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 53, no. 1, pp. 149-165, 2006.         [ Links ]

[10] S. Yu et al, "Design and Implementation of Grid Multiwing Butterfly Chaotic Attractors From a Piecewise Lorenz System," IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 57, no. 10, pp. 803-807 2010.         [ Links ]

[11] B. Bao et al., "Generation of multi-scroll hyperchaotic attractor based on Colpitts oscillator mode," Acta Physica Sinica, vol. 59, no. 3, pp. 1540-1548, 2010.         [ Links ]

[12] S. Yu, "Circuit implementation for generating three-dimensional multi-scroll chaotic attractors via triangular wave series," Acta Physica Sinica, vol. 54, no. 4, pp. 1500-1509, 2006.         [ Links ]

[13] W. Zhou et al., "Study and hardware implementation of n×m-scroll chaotic attractors," Chinese Journal of Quantum Electronics, vol. 26, no. 6, pp. 715-721, 2009.         [ Links ]

[14] G. Maggio et al., "Nonlinear analysis of the Colpitts oscillator and applications to design," IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 46, no. 9, pp. 1118-1130, 1999.         [ Links ]

[15] B. Bao et al., "Multi-scroll chaotic attractors from a modified colpitts oscillator model," International Journal of Bifurcation and Chaos, vol. 20, no. 7, pp. 2203-2211, 2010.         [ Links ]

[16] B. Bao et al., "Three-dimensional mult-scroll Colpitts chaotic system and its digital hardware implementation," Journal of Circuits and Systems, vol. 16, no. 1, pp. 69-73, 2011.         [ Links ]

[17] X. Luo et al., "Implementation of a novel twoattractor grid multi-scroll chaotic system," Chinese Physics B, vol. 19, no. 7, pp. 070510, 2010.         [ Links ]

[18] E. Campos-Cantón et al., "Multiscroll attractors by switching systems," Chaos, vol. 20, pp. 013116, 2010.         [ Links ]

[19] E. Campos-Cantón et al., "Attractors generated from switching unstable dissipative systems," Chaos, vol. 22, pp. 033121, 2012.         [ Links ]