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Solitary waves of the rotation-generalized Benjamin-Ono equation
On transverse stability of random dynamical system
1. | Center for Computational Systems Biology, Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University,Shanghai, 200433, China |
2. | Center for Computational Systems Biology, Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433 |
3. | Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433 |
References:
[1] |
J. C. Alexander, I. Kan, J. A. Yorke and Z. You, Riddled basins, Int. J. Bifurcation Chaos, 2 (1992), 795-813.
doi: 10.1142/S0218127492000446. |
[2] |
L. Arnold, "Random Dynamical Systems," Springer-Verlag Berlin Heidelberg, 1998. |
[3] |
P. Ashwin, J. Buescu and I. Stewart, From attractor to chaotic saddle: a tale of transverse instability, Nonlinearity, 9 (1996), 703-737.
doi: 10.1088/0951-7715/9/3/006. |
[4] |
P. Ashwin, E. Covas and R. Tavakol, Transverse instability for non-normal parameters, Nonlinearity, 12 (1999), 563-577.
doi: 10.1088/0951-7715/12/3/009. |
[5] |
P. Ashwin, Minimal attractors and bifurcations of random dynamical systems, Proc. Rhys. Soc. Lond. A, 455 (1999), 2615-2634.
doi: 10.1098/rspa.1999.0419. |
[6] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Autom. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[7] |
D. Cui, X. Liu, Y. Wan and X. Li, Estimation of genuine and random synchronization in multivariate neural series, Neural Networks, 23 (2010), 698-704.
doi: 10.1016/j.neunet.2010.04.003. |
[8] |
R. S. Ellis, Large deviation for a general class of random vectors, The Annals of Probability, 12 (1984), 1-12.
doi: 10.1214/aop/1176993370. |
[9] |
Y. Fang, "Stability Analysis of Linear Control Systems with Uncertain Parameters," Ph. D thesis, Case Western Reserve University, 1994. |
[10] |
S. Floyd and V. Jacobson, The synchronization of periodic routing messages, IEEE Trans. Netw, 2 (1994), 122-136. |
[11] |
V. Gazi and K. Passino, Stability analysis of social foraging swarms, IEEE Trans. SMCS-Part B: Cybernetics, 34 (2004), 539-556. |
[12] |
H. Huang, W. Daniel and Y. Qu, Robust stability of stochastic delayed additive neural networks with Markovian switching, Neural Networks, 20 (2007), 799-809.
doi: 10.1016/j.neunet.2007.07.003. |
[13] |
A. Lotka, "Elements of Physical Biology," Williams & Wilkins Company, 1925. |
[14] |
W. Lu, M. F. Atay and J. Jost, Synchronization of discrete-time dynamical networks with time-varying couplings, SIAM Journals on Mathematical Analysis, 39 (2007), 1231-1259.
doi: 10.1137/060657935. |
[15] |
W. Lu, M. F. Atay and J. Jost, Chaos synchronization in networks of coupled map with time-varying topologies, Eur. Phys. J. B, 63 (2008), 399-406.
doi: 10.1140/epjb/e2008-00023-3. |
[16] |
X. Mao, A. Matasov and A. Piunovskiy, Stochastic differential delay equations with Markovian switching, Bernoulli, 6 (2000), 73-90.
doi: 10.2307/3318634. |
[17] |
X. Mao, Exponetial stability of stochasitic delay interval systems with Markovian swithching, IEEE Trans. on Autom. Control, 47 (2002), 1604-1612. |
[18] |
G. Tang and L. Guo, Convergence of a class of multi-agent systems in probabilistic framework, Jrl Syst Sci & Complexity, 20 (2007), 173-197.
doi: 10.1007/s11424-007-9016-3. |
[19] |
L. M. Pecora and T. L. Carroll, Master stability functions for synchronized coupled systems, Phys. Rev. Lett, 80 (1998), 2109-2112.
doi: 10.1103/PhysRevLett.80.2109. |
[20] |
M. Spivak, "A Comprehensive Introduction to Differential Geometry," Houston, TX: Publish or Perish, 1970. |
[21] |
G. Ochs, "Weak Random Attractors. Technical Report," Report 449, Institut für Dynamische Systeme, Universität Bremen, 1999. |
[22] |
D. B. Johnson and D. A. Maltz, Dynamic source routing in ad hoc wireless networks, Mobile Computing, 353 (1996), 153-181.
doi: 10.1007/978-0-585-29603-6_5. |
show all references
References:
[1] |
J. C. Alexander, I. Kan, J. A. Yorke and Z. You, Riddled basins, Int. J. Bifurcation Chaos, 2 (1992), 795-813.
doi: 10.1142/S0218127492000446. |
[2] |
L. Arnold, "Random Dynamical Systems," Springer-Verlag Berlin Heidelberg, 1998. |
[3] |
P. Ashwin, J. Buescu and I. Stewart, From attractor to chaotic saddle: a tale of transverse instability, Nonlinearity, 9 (1996), 703-737.
doi: 10.1088/0951-7715/9/3/006. |
[4] |
P. Ashwin, E. Covas and R. Tavakol, Transverse instability for non-normal parameters, Nonlinearity, 12 (1999), 563-577.
doi: 10.1088/0951-7715/12/3/009. |
[5] |
P. Ashwin, Minimal attractors and bifurcations of random dynamical systems, Proc. Rhys. Soc. Lond. A, 455 (1999), 2615-2634.
doi: 10.1098/rspa.1999.0419. |
[6] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Autom. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[7] |
D. Cui, X. Liu, Y. Wan and X. Li, Estimation of genuine and random synchronization in multivariate neural series, Neural Networks, 23 (2010), 698-704.
doi: 10.1016/j.neunet.2010.04.003. |
[8] |
R. S. Ellis, Large deviation for a general class of random vectors, The Annals of Probability, 12 (1984), 1-12.
doi: 10.1214/aop/1176993370. |
[9] |
Y. Fang, "Stability Analysis of Linear Control Systems with Uncertain Parameters," Ph. D thesis, Case Western Reserve University, 1994. |
[10] |
S. Floyd and V. Jacobson, The synchronization of periodic routing messages, IEEE Trans. Netw, 2 (1994), 122-136. |
[11] |
V. Gazi and K. Passino, Stability analysis of social foraging swarms, IEEE Trans. SMCS-Part B: Cybernetics, 34 (2004), 539-556. |
[12] |
H. Huang, W. Daniel and Y. Qu, Robust stability of stochastic delayed additive neural networks with Markovian switching, Neural Networks, 20 (2007), 799-809.
doi: 10.1016/j.neunet.2007.07.003. |
[13] |
A. Lotka, "Elements of Physical Biology," Williams & Wilkins Company, 1925. |
[14] |
W. Lu, M. F. Atay and J. Jost, Synchronization of discrete-time dynamical networks with time-varying couplings, SIAM Journals on Mathematical Analysis, 39 (2007), 1231-1259.
doi: 10.1137/060657935. |
[15] |
W. Lu, M. F. Atay and J. Jost, Chaos synchronization in networks of coupled map with time-varying topologies, Eur. Phys. J. B, 63 (2008), 399-406.
doi: 10.1140/epjb/e2008-00023-3. |
[16] |
X. Mao, A. Matasov and A. Piunovskiy, Stochastic differential delay equations with Markovian switching, Bernoulli, 6 (2000), 73-90.
doi: 10.2307/3318634. |
[17] |
X. Mao, Exponetial stability of stochasitic delay interval systems with Markovian swithching, IEEE Trans. on Autom. Control, 47 (2002), 1604-1612. |
[18] |
G. Tang and L. Guo, Convergence of a class of multi-agent systems in probabilistic framework, Jrl Syst Sci & Complexity, 20 (2007), 173-197.
doi: 10.1007/s11424-007-9016-3. |
[19] |
L. M. Pecora and T. L. Carroll, Master stability functions for synchronized coupled systems, Phys. Rev. Lett, 80 (1998), 2109-2112.
doi: 10.1103/PhysRevLett.80.2109. |
[20] |
M. Spivak, "A Comprehensive Introduction to Differential Geometry," Houston, TX: Publish or Perish, 1970. |
[21] |
G. Ochs, "Weak Random Attractors. Technical Report," Report 449, Institut für Dynamische Systeme, Universität Bremen, 1999. |
[22] |
D. B. Johnson and D. A. Maltz, Dynamic source routing in ad hoc wireless networks, Mobile Computing, 353 (1996), 153-181.
doi: 10.1007/978-0-585-29603-6_5. |
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