1 |
S. Celikovsky and G. Chen, On a generalized Lorenz canonical form of chaotic systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 12 (2002), no. 8, 1789-1812.
DOI
ScienceOn
|
2 |
H. Asakura, K. Takemura, Z. Yoshida, and T. Uchida, Collisionless heating of electrons by meandering chaos and its application to a low-pressure Plasma source, Jpn. J. Appl. Phys. 36 (1997), 4493-4496.
DOI
|
3 |
S. Celikovsky and G. Chen, On the generalized Lorenz canonical form, Chaos Solitons Fractals 26 (2005), no. 5, 1271-1276.
DOI
ScienceOn
|
4 |
S. Celikovsky and A. Vaecek, Bilinear systems and chaos, Kybernetika 30 (1994), no. 4, 403-424.
|
5 |
S. Celikovsky and A. Vaecek, Control Systems: from linear analysis to synthesis of chaos, London, Prentice-Hall, 1996.
|
6 |
G. Chen and T. Ueta, Yet another chaotic attractor, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 9 (1999), no. 7, 1465-1466.
DOI
|
7 |
G. Chen and T. Ueta, Bifurcation analysis of Chen's equation, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 10 (2000), no. 8, 1917-1931.
|
8 |
L. O. Chua, M. Itoh, L. Kovurev, and K. Eckert, Chaos synchronization in Chua's circuit, J. Circuits Systems Comput. 3 (1993), no. 1, 93-108.
DOI
|
9 |
T. Li, G. Chen, and Y. Tang, Complex dynamical behaviors of the chaotic Chen's system, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003), no. 9, 2561-2574.
DOI
ScienceOn
|
10 |
K. Huang and G. Yang, Stability and Hopf bifurcation analysis of a new system, Chaos Solitons Fractals 39 (2009), no. 2, 567-578.
DOI
ScienceOn
|
11 |
Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, second edition, Springer-Verlag, New York, 1998.
|
12 |
C. Li and G. Chen, A note on Hopf bifurcation in Chen's system, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13 (2003), no. 6, 1609-1615.
DOI
|
13 |
T. Li, G. Chen, and Y. Tang, On stability and bifurcation of Chen's system, Chaos Solitons Fractals 19 (2004), no. 5, 1269-1282.
DOI
ScienceOn
|
14 |
X. Li and Q. Ou, Dynamical properties and simulation of a new Lorenz-like chaotic system, Nonlinear Dynam. 65 (2011), no. 3, 255-270.
DOI
|
15 |
C. Liu, T. Liu, L. Liu, and K. Liu, A new chaotic attractor, Chaos Solitons Fractals 22 (2004), no. 5 1031-1038.
DOI
ScienceOn
|
16 |
E. N. Lorenz, Deterministic non-periodic flow, J. Atmospheric Sci. 20 (1963), 130-141.
DOI
|
17 |
J. Lu, G. Chen, and S. Zhang, The compound structure of a new chaotic attractor, Chaos Solitons Fractals 14 (2002), no. 5, 669-672.
DOI
ScienceOn
|
18 |
J. Lu, T. Zhou, G. Chen, and S. Zhang, Local bifurcations of the Chen system, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 12 (2002), no. 10, 2257-2270.
DOI
ScienceOn
|
19 |
J. M. Ottino, C. W.Leong, H. Rising, and P. D. Swanson, Morphological structures produced by mixing in chaotic flows, Nature 333 (1988), 419-425.
DOI
ScienceOn
|
20 |
B. Munmuangsaen and B. Srisuchinwong, A new five-term simple chaotic attractor, Phys. Lett. A 373 (2009), 4038-4043.
DOI
ScienceOn
|
21 |
O. E. Rossler, An equation for continuous chaos, Phys. Lett. A 57 (1976), 397-398.
DOI
ScienceOn
|
22 |
C. P. Silva, Silnikov theorem-a tutorial, IEEE Trans. Circuits Systems I Fund. Theory Appl. 40 (1993), no. 10, 657-682.
DOI
ScienceOn
|
23 |
L. P. Silnikov, A case of the existence of a countable number of periodic motions, Sov. Math. Docklady 6 (1965), 163-166.
|
24 |
J. C. Sprott, Simplest dissipative chaotic flow, Phys. Lett. A 228 (1997), no. 4-5, 271-274.
DOI
ScienceOn
|
25 |
L. P. Silnikov, A contribution of the problem of the structure of an extended neighborhood of rough equilibrium state of saddle-focus type, Math. USSR-Shornik 10 (1970), 91-102.
DOI
ScienceOn
|
26 |
C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Applied Mathematical Sciences, 41. Springer-Verlag, New York-Berlin, 1982.
|
27 |
J. C. Sprott, Some simple chaotic flows, Phys. Rev. E (3) 50 (1994), no. 2, R647-R650.
DOI
|
28 |
J. C. Sprott, A new class of chaotic circuit, Phys. Lett. A 266 (2000), 19-23.
DOI
ScienceOn
|
29 |
G. van der Schrier and L. Maas, The diffusionless Lorenz equations; Shilnikov bifurcations and reduction to an explicit map, Phys. D 141 (2000), no. 1-2, 19-36.
DOI
ScienceOn
|
30 |
G. Tigan and D. Constantinescu, Heteroclinic orbits in the T and the Lu system, Chaos Solitons Fractals 42 (2009), no. 1, 20-23.
DOI
ScienceOn
|
31 |
Z. Wei and Q. Yang, Dynamics of a new autonomous 3-D chaotic system only with stable equilibria, Nonl. Anal.: Real World Applications 12 (2011), 106-118.
DOI
|
32 |
Q. Yang and G. Chen, A chaotic system with one saddle and two stable node-foci, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 18 (2008), no. 5, 1393-1414.
DOI
ScienceOn
|
33 |
Q. Yang, G. Chen, and Y. Zhou, A unified Lorenz-type system and its canonical form, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 16 (2006), no. 10, 2855-1871.
DOI
ScienceOn
|
34 |
Y. Yu and S. Zhang, Hopf bifurcation in the Lu system, Chaos Solitons Fractals 17 (2003), no. 5, 901-906.
DOI
ScienceOn
|
35 |
Y. Yu and S. Zhang, Hopf bifurcation analysis of the Lu system, Chaos Solitons Fractals 21 (2004), no. 5, 1215-1220.
DOI
ScienceOn
|
36 |
A.Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Determining Lyapunov exponents from a time series, Phys. D 16 (1985), no. 3, 285-317.
DOI
ScienceOn
|
37 |
S. Celikovsky and G. Chen, Hyperbolic-type generalized Lorenz system and its canonical form, Proc. 15th Triennial World Congrss of IFAC, Barcelona, Spain, (2002b), in CD ROM.
|
38 |
G. Alvarez, S. Li, F. Montoya, G. Pastor, and M. Romera, Breaking projective chaos sychronization secure communication using filtering and generalized synchronization, Chaos Solitons Fractals 24 (2005), no. 3, 775-783.
DOI
ScienceOn
|
39 |
J. Lu and G. Chen, A new chaotic attractor coined, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 12 (2002), no. 3, 659-661.
DOI
ScienceOn
|