Topological analysis of chaotic solution of a three-element memristive circuit

International Journal of Bifurcation and Chaos

Volumn 20, Issue 11, 2010, Pages 3819-3827

  Ginoux, Jean Marc ^a   Letellier, Christophe ^b   Chua, Leon O ^c  

^a Univ du Sud   (France)

^b UNIVERSITÉ DE ROUEN   (France)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

chaos; electronic circuit; Memristor; topological analysis

Indexed keywords

CHAOS THEORY; DYNAMICAL SYSTEMS; MEMRISTORS; NETWORKS (CIRCUITS); TIMING CIRCUITS;

CHAOTIC ATTRACTORS; CHAOTIC SOLUTIONS; MEMRISTOR; TOPOLOGICAL ANALYSIS;

TOPOLOGY;

EID: 78651562179     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127410027878     Document Type: Article

References (19)

1. Chua, L. O. [1971] "Memristor-The missing circuit element," IEEE Trans. Circuit Th. 18, 507-519.
2. Chua, L. O. & Kang, S. M. [1976] "Memristive devices and systems," Proc. IEEE 64, 209-223.
3. Gilmore, R. [1998] "Topological analysis of chaotic dynamical systems," Rev. Mod. Phys. 70, 1455-1529.
4. Gilmore, R., Ginoux, J.-M., Jones, T., Letellier, C. & Freitas, U. S. [2010] "Connecting curves for dynamical systems," J. Phys. A 43, 255101.
5. Ginoux, J.-M. [2009] Differential Geometry Applied to Dynamical Systems, World Scientific Series on Nonlinear Science, Series A, Vol. 66 (World Scientific, Singapore).
6. Ginoux, J.-M. & Letellier, C. [2009] "Flow curvature manifolds for shaping chaotic attractors: I. Riosslerlike systems," J. Phys. A 42, 285101.
7. Itoh, M. & Chua, L. O. [2008] "Memristor oscillators," Int. J. Bifurcation and Chaos 18, 3183-3206.
8. Le Sceller, L., Letellier, C. & Gouesbet, G. [1994] "Algebraic evaluation of linking numbers of unstable periodic orbits in chaotic attractors," Phys. Rev. E 49, 4693-4695.
9. Letellier, C., Dutertre, P. & Maheu, B. [1995] "Unstable periodic orbits and templates of the Riossler system: Toward a systematic topological characterization," Chaos 5, 271-282.
10. Malasoma, J.-M. & Letellier, C. [2010] in preparation.
11. Muthuswamy, B. & Chua, L. O. [2010] "Simplest chaotic circuit," Int. J. Bifurcation and Chaos 20, 1567-1580.
12. Muthuswamy, B. & Kakate, P. P. [2010] "Memristorbased chaotic circuits," IETE Techn. Rev. 26, 417-429.
13. Roth, M. & Peikert, R. [1998] "A higher-order method for finding vortex core lines," Proc. IEEE Conf. Vizualization'98, pp. 143-150.
14. Sprott, J. C. [1994] "Some simple chaotic flows," Phys. Rev. E 50, 647-650.
15. Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. [2008] "The missing memristor found," Nature 453, 80-83.
16. Thomas, R. & Kaufman, M. [2001] "Multistationarity, the basis of cell differentiation and memory: I. Structural conditions of multistationarity and other nontrivial behavior," Chaos 11, 170-179.
17. Tufillaro, N. B., Abbott, T. & Reilly, J. [1992] An Experimental Approach to Nonlinear Dynamics and Chaos (Addison-Wesley, NY).
18. van der Schrier, G. & Maas, L. R. M. [2000] "The diffusionless Lorenz equations; Shil'nikov bifurcations and reduction to an explicit map," Physica D 141, 19-36.
19. Zhang, F. & Heidel, J. [1997] "Non chaotic behaviour in three-dimensional quadratic systems," Nonlinearity 10, 1289-1303.