## Abstract

We study the onset of synchronization in a network of *N* delay-coupled stochastic fiber ring lasers with respect to various parameters when the coupling power is weak. In particular, for groups of three or more ring lasers mutually coupled to a central hub laser, we demonstrate a robust tendency toward out-of-phase (achronal) synchronization between the *N* – 1 outer lasers and the single inner laser. In contrast to the achronal synchronization, we find the outer lasers synchronize with zero-lag (isochronal) with respect to each other, thus forming a set of *N* – 1 coherent fiber lasers.

© 2011 OSA

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### References

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- M. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 289–289 (1977).

[Crossref] - M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).

[Crossref] [PubMed] - K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).

[Crossref] - R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).

[Crossref] - D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).

[Crossref] - M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).

[Crossref] [PubMed] - M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).

[Crossref] - A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).

[Crossref] [PubMed] - O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).

[Crossref] - J. Mulet, C. Mirasso, T. Heil, and I. Fischer, “Synchronication scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quantum Semiclass. Opt. 6, 97–105 (2004).

[Crossref] - T. Heil, I. Fischer, W. Elsasser, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett.86, 795–798 (2001).

[Crossref] [PubMed] - J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).

[Crossref] -
Q. L. Williams and R. Roy, “Fast polarization dynamics of an erbium-doped fiber ring laser,” Opt. Lett. 21, 1478–1480 (1996).

[Crossref] [PubMed] - Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).

[Crossref] - G. D. Vanwiggeren and R. Roy, “Chaotic communication using time-delayed optical systems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2129–2156 (1999).

[Crossref] - R. Wang and K. Shen, “Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them,” Phys. Rev. E 65, 016207 (2002).

[Crossref] - Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).

[Crossref] - D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).

[Crossref] - L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).

[Crossref] - I. B. Schwartz and L. B. Shaw, “Isochronal synchronization of delay-coupled systems,” Phys. Rev. E 75, 046207 (2007).

[Crossref] - A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).

[Crossref] [PubMed] - C. Massoller and A. Marti, “Random delays and the sychronization of chaotic maps,” Phys. Rev. Lett. 94, 134102 (2005).

[Crossref] - E. A. Rogers, “Synchronization of high dimensional dynamical systems,” Ph.D. thesis, University of Maryland College Park (2005).

- E. A. Rogers-Dakin, J. Garcia-Ojalvo, D. J. Deshazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 (2006).

[Crossref] - A. S. Landsman and I. B. Schwartz, “Complete chaotic synchronization in mutually coupled time-delay systems,” Phys. Rev. E 75, 026201 (2007).

[Crossref] - J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105, 264101 (2010).

[Crossref] - D. Tsygankov and K. Wiesenfeld, “Weak link synchronization,” Phys. Rev. E 73, 026222 (2006).

[Crossref] - L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Phys. Rev. Lett. 76, 1816–1819 (1996).

[Crossref] [PubMed]

#### 2010 (2)

O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).

[Crossref]

J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105, 264101 (2010).

[Crossref]

#### 2007 (4)

A. S. Landsman and I. B. Schwartz, “Complete chaotic synchronization in mutually coupled time-delay systems,” Phys. Rev. E 75, 026201 (2007).

[Crossref]

I. B. Schwartz and L. B. Shaw, “Isochronal synchronization of delay-coupled systems,” Phys. Rev. E 75, 046207 (2007).

[Crossref]

A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).

[Crossref]
[PubMed]

A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).

[Crossref]
[PubMed]

#### 2006 (3)

L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).

[Crossref]

E. A. Rogers-Dakin, J. Garcia-Ojalvo, D. J. Deshazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 (2006).

[Crossref]

D. Tsygankov and K. Wiesenfeld, “Weak link synchronization,” Phys. Rev. E 73, 026222 (2006).

[Crossref]

#### 2005 (1)

C. Massoller and A. Marti, “Random delays and the sychronization of chaotic maps,” Phys. Rev. Lett. 94, 134102 (2005).

[Crossref]

#### 2004 (2)

D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).

[Crossref]

J. Mulet, C. Mirasso, T. Heil, and I. Fischer, “Synchronication scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quantum Semiclass. Opt. 6, 97–105 (2004).

[Crossref]

#### 2003 (1)

Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).

[Crossref]

#### 2002 (2)

R. Wang and K. Shen, “Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them,” Phys. Rev. E 65, 016207 (2002).

[Crossref]

J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).

[Crossref]

#### 2001 (1)

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).

[Crossref]
[PubMed]

#### 2000 (1)

D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).

[Crossref]

#### 1999 (1)

G. D. Vanwiggeren and R. Roy, “Chaotic communication using time-delayed optical systems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2129–2156 (1999).

[Crossref]

#### 1997 (2)

Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).

[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).

[Crossref]

#### 1996 (3)

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).

[Crossref]
[PubMed]

Q. L. Williams and R. Roy, “Fast polarization dynamics of an erbium-doped fiber ring laser,” Opt. Lett. 21, 1478–1480 (1996).

[Crossref]
[PubMed]

L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Phys. Rev. Lett. 76, 1816–1819 (1996).

[Crossref]
[PubMed]

#### 1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).

[Crossref]

#### 1979 (1)

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).

[Crossref]

#### 1977 (1)

M. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 289–289 (1977).

[Crossref]

#### Bertram, M.

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).

[Crossref]
[PubMed]

#### Buldu, J. M.

A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).

[Crossref]
[PubMed]

#### Danckaert, J.

O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).

[Crossref]

#### Deshazer, D. J.

E. A. Rogers-Dakin, J. Garcia-Ojalvo, D. J. Deshazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 (2006).

[Crossref]

D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).

[Crossref]

#### Elsasser, W.

T. Heil, I. Fischer, W. Elsasser, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett.86, 795–798 (2001).

[Crossref]
[PubMed]

#### Ertl, G.

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).

[Crossref]
[PubMed]

#### Fischer, I.

O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).

[Crossref]

J. Mulet, C. Mirasso, T. Heil, and I. Fischer, “Synchronication scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quantum Semiclass. Opt. 6, 97–105 (2004).

[Crossref]

T. Heil, I. Fischer, W. Elsasser, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett.86, 795–798 (2001).

[Crossref]
[PubMed]

#### Franz, A. L.

A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).

[Crossref]
[PubMed]

#### Garcia-Ojalvo, J.

J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105, 264101 (2010).

[Crossref]

E. A. Rogers-Dakin, J. Garcia-Ojalvo, D. J. Deshazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 (2006).

[Crossref]

Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).

[Crossref]

#### Glass, L.

M. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 289–289 (1977).

[Crossref]

#### Heil, T.

J. Mulet, C. Mirasso, T. Heil, and I. Fischer, “Synchronication scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quantum Semiclass. Opt. 6, 97–105 (2004).

[Crossref]

T. Heil, I. Fischer, W. Elsasser, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett.86, 795–798 (2001).

[Crossref]
[PubMed]

#### Huys, O. D.

[Crossref]

#### Ikeda, K.

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).

[Crossref]

#### Imai, Y.

Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).

[Crossref]

#### Imoto, T.

Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).

[Crossref]

#### Johnston, G. L.

D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).

[Crossref]

#### Kim, M.

[Crossref]
[PubMed]

#### Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).

[Crossref]

#### Kocarev, L.

L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Phys. Rev. Lett. 76, 1816–1819 (1996).

[Crossref]
[PubMed]

#### Kurths, J.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).

[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).

[Crossref]
[PubMed]

#### Kurths, M.

D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).

[Crossref]

#### Landsman, A. S.

A. S. Landsman and I. B. Schwartz, “Complete chaotic synchronization in mutually coupled time-delay systems,” Phys. Rev. E 75, 026201 (2007).

[Crossref]

#### Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).

[Crossref]

#### Mackey, M.

M. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 289–289 (1977).

[Crossref]

#### Marti, A.

C. Massoller and A. Marti, “Random delays and the sychronization of chaotic maps,” Phys. Rev. Lett. 94, 134102 (2005).

[Crossref]

#### Masoller, C.

J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105, 264101 (2010).

[Crossref]

#### Massoller, C.

C. Massoller and A. Marti, “Random delays and the sychronization of chaotic maps,” Phys. Rev. Lett. 94, 134102 (2005).

[Crossref]

#### Matus, M.

J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).

[Crossref]

#### Mikhailov, A. S.

[Crossref]
[PubMed]

#### Mirasso, C.

[Crossref]

#### Mirasso, C. R.

[Crossref]
[PubMed]

#### Moloney, J. V.

J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).

[Crossref]

#### Mulet, J.

[Crossref]

[Crossref]
[PubMed]

#### Murakawa, H.

[Crossref]

#### Parlitz, U.

L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Phys. Rev. Lett. 76, 1816–1819 (1996).

[Crossref]
[PubMed]

#### Pikovsky, A. S.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).

[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).

[Crossref]
[PubMed]

#### Pollmann, M.

[Crossref]
[PubMed]

#### Reddy, D. V. R.

D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).

[Crossref]

#### Rogers, E. A.

L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).

[Crossref]

E. A. Rogers, “Synchronization of high dimensional dynamical systems,” Ph.D. thesis, University of Maryland College Park (2005).

#### Rogers-Dakin, E. A.

[Crossref]

#### Rosenblum, M. G.

[Crossref]

[Crossref]
[PubMed]

#### Rotermund, H. H.

[Crossref]
[PubMed]

#### Roy, R.

[Crossref]

A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).

[Crossref]
[PubMed]

L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).

[Crossref]

[Crossref]

[Crossref]

G. D. Vanwiggeren and R. Roy, “Chaotic communication using time-delayed optical systems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2129–2156 (1999).

[Crossref]

Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).

[Crossref]

Q. L. Williams and R. Roy, “Fast polarization dynamics of an erbium-doped fiber ring laser,” Opt. Lett. 21, 1478–1480 (1996).

[Crossref]
[PubMed]

#### Sanjuan, M.

A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).

[Crossref]
[PubMed]

#### Schwartz, I. B.

A. S. Landsman and I. B. Schwartz, “Complete chaotic synchronization in mutually coupled time-delay systems,” Phys. Rev. E 75, 026201 (2007).

[Crossref]

I. B. Schwartz and L. B. Shaw, “Isochronal synchronization of delay-coupled systems,” Phys. Rev. E 75, 046207 (2007).

[Crossref]

[Crossref]
[PubMed]

[Crossref]

#### Sen, A.

[Crossref]

#### Shaw, L. B.

[Crossref]
[PubMed]

I. B. Schwartz and L. B. Shaw, “Isochronal synchronization of delay-coupled systems,” Phys. Rev. E 75, 046207 (2007).

[Crossref]

[Crossref]

#### Shen, K.

R. Wang and K. Shen, “Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them,” Phys. Rev. E 65, 016207 (2002).

[Crossref]

#### Tighe, B. P.

[Crossref]

#### Tsygankov, D.

D. Tsygankov and K. Wiesenfeld, “Weak link synchronization,” Phys. Rev. E 73, 026222 (2006).

[Crossref]

#### Vanwiggeren, G. D.

G. D. Vanwiggeren and R. Roy, “Chaotic communication using time-delayed optical systems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2129–2156 (1999).

[Crossref]

#### Vicente, R.

[Crossref]

#### von Oertzen, A.

[Crossref]
[PubMed]

#### Wagemakers, A.

[Crossref]
[PubMed]

#### Wang, R.

R. Wang and K. Shen, “Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them,” Phys. Rev. E 65, 016207 (2002).

[Crossref]

#### White, J. K.

[Crossref]

#### Wiesenfeld, K.

D. Tsygankov and K. Wiesenfeld, “Weak link synchronization,” Phys. Rev. E 73, 026222 (2006).

[Crossref]

#### Williams, Q. L.

[Crossref]

Q. L. Williams and R. Roy, “Fast polarization dynamics of an erbium-doped fiber ring laser,” Opt. Lett. 21, 1478–1480 (1996).

[Crossref]
[PubMed]

#### Zamora-Munt, J.

[Crossref]

#### Chaos (3)

[Crossref]
[PubMed]

[Crossref]

[Crossref]

#### IEEE J. Quantum Electron. (1)

[Crossref]

#### IEEE J. Sel. Top. Quantum Electron. (1)

[Crossref]

#### Int. J. Bifurcation Chaos Appl. Sci. Eng. (1)

[Crossref]

#### J. Opt. B: Quantum Semiclass. Opt. (1)

[Crossref]

#### Opt. Commun. (2)

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).

[Crossref]

[Crossref]

#### Opt. Lett. (1)

[Crossref]
[PubMed]

#### Phys. Rev. A (1)

[Crossref]

#### Phys. Rev. E (6)

[Crossref]

[Crossref]

[Crossref]

[Crossref]

[Crossref]

[Crossref]

#### Phys. Rev. Lett. (7)

[Crossref]
[PubMed]

[Crossref]
[PubMed]

[Crossref]

[Crossref]

[Crossref]

[Crossref]
[PubMed]

[Crossref]

#### Science (2)

[Crossref]

[Crossref]
[PubMed]

#### Other (2)

[Crossref]
[PubMed]

E. A. Rogers, “Synchronization of high dimensional dynamical systems,” Ph.D. thesis, University of Maryland College Park (2005).

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### Figures (4)

**Fig. 1**

The cross correlation and phase coherence for _{s}_{d}_{out}_{in}_{d}

**Fig. 2**

A time history of the intensity for a numerical experiment with

**Fig. 3**

Here we demonstrate the growth of the cross-correlation for _{out}_{s}

**Fig. 4**

Achronal synchronization for the weak pumping case. Here the outer lasers have _{out}

### Tables (1)

**Table 1** Summary of parameters used in the laser coupling model. The detuning parameter of the outer lasers was uniform, _{out}_{in}

### Equations (8)

Equations on this page are rendered with MathJax. Learn more.