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Multiobjective synchronization of coupled systems
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10.1063/1.3595701
/content/aip/journal/chaos/21/2/10.1063/1.3595701
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/2/10.1063/1.3595701

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Illustration of the optimal Pareto front and the relationship between dominated and nondominated solutions.

Image of FIG. 2.
FIG. 2.

(Color online) Encoding scheme of multiobjective synchronization.

Image of FIG. 3.
FIG. 3.

(Color online) Synchronization errors of chaotic systems (errors plotted in log10) and solutions (Computing f 1 and f 2) obtained by adaptive strategy and MNSGA-II. In (b), (d), and (f), black lines are the errors by adaptive strategy; other color lines are the corresponding synchronization errors using the same solutions by MNSGA-II. (a) Solutions obtained by adaptive strategy and MNSGA-II for synchronization of the Rössler system; (b) synchronization errors of the Rössler system using adaptive strategy and MNSGA-II; (c) solutions obtained by adaptive strategy and MNSGA-II for synchronization of DCNN; (d) synchronization errors of DCNN using adaptive strategy and MNSGA-II (black lines are the errors by adaptive strategy); (e) solutions obtained by adaptive strategy and MNSGA-II for synchronization of the hyperchaotic Rössler system; (f) synchronization errors of the hyperchaotic Rössler system using adaptive strategy and MNSGA-II (black lines are the errors by adaptive strategy).

Image of FIG. 4.
FIG. 4.

(Color online) Synchronization errors of chaotic systems (errors plotted in log10) and solutions (Computing f 1 and f 2) obtained by adaptive strategy and MNSGA-II with constrained Γ. In (b), (d) and (f), black lines are the errors by adaptive strategy; other color lines are the corresponding synchronization errors using the same solutions by MNSGA-II. (a) Solutions obtained by adaptive strategy and MNSGA-II for synchronization of the Rössler system; (b) synchronization errors of the Rössler system using adaptive strategy and MNSGA-II; (c) solutions obtained by adaptive strategy and MNSGA-II for synchronization of DCNN; (d) synchronization errors of DCNN using adaptive strategy and MNSGA-II (black lines are the errors by adaptive strategy); (e) solutions obtained by adaptive strategy and MNSGA-II for synchronization of the hyperchaotic Rössler system; (f) synchronization errors of the hyperchaotic Rössler system using adaptive strategy and MNSGA-II (black lines are the errors by adaptive strategy).

Image of FIG. 5.
FIG. 5.

(Color online) Convergence comparison of NSGA-II and MNSGA-II for the Rössler system with unconstrained Γ.

Image of FIG. 6.
FIG. 6.

(Color online) Convergence comparison of NSGA-II and MNSGA-II for the hyperchaotic Rössler system with unconstrained Γ.

Image of FIG. 7.
FIG. 7.

(Color online) Convergence comparison of NSGA-II and MNSGA-II for the Rössler system with constrained Γ.

Image of FIG. 8.
FIG. 8.

(Color online) Convergence comparison of NSGA-II and MNSGA-II for the hyperchaotic Rössler system with constrained Γ.

Image of FIG. 9.
FIG. 9.

(Color online) Synchronization error of DCNN when using different coupling strength.

Tables

Generic image for table
Table I.

The initial values of sender (IVS) and initial values of receiver (IVR).

Generic image for table
Table II.

Synchronization of the Rössler system with different Γ using adaptive coupling and MNSGA-II.

Generic image for table
Table III.

Synchronization of DCNNs with different Γ using adaptive coupling and MNSGA-II.

Generic image for table
Table IV.

Synchronization of the hyperchaotic Rössler system with different Γ using adaptive coupling and MNSGA-II.

Generic image for table
Table V.

Synchronization of the Rössler system with different Γ using adaptive coupling and MNSGA-II.

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/content/aip/journal/chaos/21/2/10.1063/1.3595701
2011-06-28
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Multiobjective synchronization of coupled systems
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/2/10.1063/1.3595701
10.1063/1.3595701
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