Symmetry types and phase-shift synchrony in networks
In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to t...
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| Autor*in: |
Golubitsky, Martin [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016transfer abstract |
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| Umfang: |
10 |
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| Übergeordnetes Werk: |
Enthalten in: Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation - Thude, Hansjörg ELSEVIER, 2015transfer abstract, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:320 ; year:2016 ; day:15 ; month:04 ; pages:9-18 ; extent:10 |
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| DOI / URN: |
10.1016/j.physd.2015.12.005 |
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| 520 | |a In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. | ||
| 520 | |a In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. | ||
| 650 | 7 | |a Periodic solutions |2 Elsevier | |
| 650 | 7 | |a Phase-shift synchrony |2 Elsevier | |
| 650 | 7 | |a Coupled cell networks |2 Elsevier | |
| 650 | 7 | |a Symmetry |2 Elsevier | |
| 700 | 1 | |a Matamba Messi, Leopold |4 oth | |
| 700 | 1 | |a Spardy, Lucy E. |4 oth | |
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10.1016/j.physd.2015.12.005 doi GBVA2016006000016.pica (DE-627)ELV040010635 (ELSEVIER)S0167-2789(15)00266-3 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Golubitsky, Martin verfasserin aut Symmetry types and phase-shift synchrony in networks 2016transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. Periodic solutions Elsevier Phase-shift synchrony Elsevier Coupled cell networks Elsevier Symmetry Elsevier Matamba Messi, Leopold oth Spardy, Lucy E. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:320 year:2016 day:15 month:04 pages:9-18 extent:10 https://doi.org/10.1016/j.physd.2015.12.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 320 2016 15 0415 9-18 10 045F 530 |
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10.1016/j.physd.2015.12.005 doi GBVA2016006000016.pica (DE-627)ELV040010635 (ELSEVIER)S0167-2789(15)00266-3 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Golubitsky, Martin verfasserin aut Symmetry types and phase-shift synchrony in networks 2016transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. Periodic solutions Elsevier Phase-shift synchrony Elsevier Coupled cell networks Elsevier Symmetry Elsevier Matamba Messi, Leopold oth Spardy, Lucy E. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:320 year:2016 day:15 month:04 pages:9-18 extent:10 https://doi.org/10.1016/j.physd.2015.12.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 320 2016 15 0415 9-18 10 045F 530 |
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10.1016/j.physd.2015.12.005 doi GBVA2016006000016.pica (DE-627)ELV040010635 (ELSEVIER)S0167-2789(15)00266-3 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Golubitsky, Martin verfasserin aut Symmetry types and phase-shift synchrony in networks 2016transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. Periodic solutions Elsevier Phase-shift synchrony Elsevier Coupled cell networks Elsevier Symmetry Elsevier Matamba Messi, Leopold oth Spardy, Lucy E. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:320 year:2016 day:15 month:04 pages:9-18 extent:10 https://doi.org/10.1016/j.physd.2015.12.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 320 2016 15 0415 9-18 10 045F 530 |
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10.1016/j.physd.2015.12.005 doi GBVA2016006000016.pica (DE-627)ELV040010635 (ELSEVIER)S0167-2789(15)00266-3 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Golubitsky, Martin verfasserin aut Symmetry types and phase-shift synchrony in networks 2016transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. Periodic solutions Elsevier Phase-shift synchrony Elsevier Coupled cell networks Elsevier Symmetry Elsevier Matamba Messi, Leopold oth Spardy, Lucy E. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:320 year:2016 day:15 month:04 pages:9-18 extent:10 https://doi.org/10.1016/j.physd.2015.12.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 320 2016 15 0415 9-18 10 045F 530 |
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10.1016/j.physd.2015.12.005 doi GBVA2016006000016.pica (DE-627)ELV040010635 (ELSEVIER)S0167-2789(15)00266-3 DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Golubitsky, Martin verfasserin aut Symmetry types and phase-shift synchrony in networks 2016transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. Periodic solutions Elsevier Phase-shift synchrony Elsevier Coupled cell networks Elsevier Symmetry Elsevier Matamba Messi, Leopold oth Spardy, Lucy E. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:320 year:2016 day:15 month:04 pages:9-18 extent:10 https://doi.org/10.1016/j.physd.2015.12.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 320 2016 15 0415 9-18 10 045F 530 |
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Enthalten in Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation Amsterdam [u.a.] volume:320 year:2016 day:15 month:04 pages:9-18 extent:10 |
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Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation |
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Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. 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In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. |
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In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. |
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In this paper we discuss what is known about the classification of symmetry groups and patterns of phase-shift synchrony for periodic solutions of coupled cell networks. Specifically, we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of R n (coupled equations), T n (coupled oscillators), and ( R k ) n where k ≥ 2 (coupled systems). To do this we use the H / K Theorem of Buono and Golubitsky (2001) applied to coupled equations and coupled systems and prove the H / K theorem in the case of coupled oscillators. Josić and Török (2006) prove that the H / K lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems. We show that the corresponding theorem is false for coupled equations. We also prove that the pairs of subgroups H ⊃ K for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems. Finally, we prove that patterns of rigid phase-shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems. |
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