Modelling and simulation of the multi-scroll chaotic attractors using bond graph technique

Abstract This paper presents modelling and simulation of multi-scroll chaotic attractors by using a new simple and more general bond graph model. For this purpose, the multi-segment non-linear resistor in Chua’s circuit is modelled by using piecewise linearization with control inequalities. The proposed model consists of active/passive circuit elements, voltage-controlled current source (VCCS) and ideal switches. The advantage of modelling multi-segment non-linear resistor by using control inequalities yields minimum number of the switches and sources. Proposed model is simple and more general and, especially, could be used in various kinds of non-linear circuit in the chaos studies. Generally, two different non-linear resistor models are used in the literature to obtain odd and even numbers of the scrolls. In this study, one model is developed for both multi-scroll chaotic attractors. In this paper, bond graph simulation of Chua’s circuit is realized by using proposed model. The BONDAS program that developed in Matlab is used for the simulations, and satisfactory results are obtained.

[1]  Kim-Fung Man,et al.  A Systematic Approach to Generating n-scroll attractors , 2002, Int. J. Bifurc. Chaos.

[2]  Guanrong Chen,et al.  Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications , 2006 .

[3]  Muhammet Köksal,et al.  Derivation of state and output equations for systems containing switches and a novel definition of a switch using the bond graph model , 1997 .

[4]  Fikret Ata,et al.  The multi-mode chaotic behaviors: N+N and 2D N-scroll chaotic attractors , 2006 .

[5]  Guanrong Chen,et al.  Theoretical Design and Circuit Implementation of Multidirectional Multi-Torus Chaotic Attractors , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Arif Gülten,et al.  Examination of chaotic behaviours using bond graph model , 2003, J. Frankl. Inst..

[7]  Wolfgang Borutzky.  Bond graph modelling and simulation of multidisciplinary systems - An introduction , 2009, Simul. Model. Pract. Theory.

[8]  Johan A. K. Suykens,et al.  Families of scroll Grid attractors , 2002, Int. J. Bifurc. Chaos.

[9]  Alan S. Perelson,et al.  Introduction to Bond Graphs and Their Applications , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Xinghuo Yu,et al.  Design and analysis of multiscroll chaotic attractors from saturated function series , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Dean Karnopp,et al.  Analysis and simulation of multiport systems : the bond graph approach to physical system dynamics , 1968 .

[12]  Henry Leung,et al.  Design and implementation of n-scroll chaotic attractors from a general jerk circuit , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Guanrong Chen,et al.  Generation of n-scroll attractors via sine function , 2001 .

[14]  G. Dauphin-Tanguy,et al.  Electrothermal bond graph model for semiconductor switching devices , 1996, Proceedings of Applied Power Electronics Conference. APEC '96.

[15]  Jean Buisson,et al.  Analysis of switching devices with bond graphs , 1993 .

[16]  Johan A. K. Suykens,et al.  Quasilinear approach to nonlinear systems and the design of n-double scroll (n=1, 2, 3, 4, . . .) , 1991 .

[17]  Muhammet Köksal,et al.  Analysis of switched systems using the bond graph methods , 1999 .

[18]  Dean Karnopp,et al.  Introduction to physical system dynamics , 1983 .

[19]  Ahmed S. Elwakil,et al.  Generation of n-scroll chaos using nonlinear transconductors , 2003, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03..

[20]  J. R. Hewit,et al.  ACE: a bond graph modelling and development tool for control system design and implementation , 2000 .

[21]  Jesús Félez,et al.  Efficient simulation of mechanism kinematics using bond graphs , 2009, Simul. Model. Pract. Theory.

[22]  Henry Leung,et al.  Experimental verification of multidirectional multiscroll chaotic attractors , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  Laurent Lefèvre,et al.  Basis for bond-graph modeling in chemical engineering , 2007 .

[24]  Loganathan Umanand,et al.  Modelling of switched mode power converters using bond graph , 2005 .

[25]  Johan A. K. Suykens,et al.  n-scroll chaos generators: a simple circuit model , 2001 .

[26]  Loganathan Umanand,et al.  Modelling of switching systems in bond graphs using the concept of switched power junctions , 2005, J. Frankl. Inst..

[27]  G. Dauphin-Tanguy,et al.  Bond graph modelling of a photovoltaic system feeding an induction motor-pump , 2007, Simul. Model. Pract. Theory.

[28]  Jean Buisson,et al.  Bond graph modelling of hard nonlinearities in mechanics: A hybrid approach , 2008 .

[29]  Patricia V. Lawford,et al.  Systemic modelling and computational physiology: The application of Bond Graph boundary conditions for 3D cardiovascular models , 2009, Simul. Model. Pract. Theory.

[30]  Xinghuo Yu,et al.  n-scroll chaotic oscillators by second-order systems and double-hysteresis blocks , 2003 .

[31]  Ahmed S. Elwakil,et al.  n-scroll chaos generator using nonlinear transconductor , 2002 .

[32]  Michael Peter Kennedy,et al.  Robust OP Amp Realization of Chua's Circuit , 1992 .

[33]  J. Buisson,et al.  Analysis of the bond graph model of hybrid physical systems with ideal switches , 2002 .

[34]  Guanrong Chen,et al.  Experimental confirmation of n-scroll hyperchaotic attractors , 2006, 2006 IEEE International Symposium on Circuits and Systems.