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Junge, “An adaptive subdivision technique for the approximation of attractors and invariant measures,” <i>Computing and Visualization in Science</i>, pp. 63–68, 1998."},"page":"63-68","year":"1998","publication_status":"published","publication_identifier":{"issn":["1432-9360","1433-0369"]},"doi":"10.1007/s007910050006","title":"An adaptive subdivision technique for the approximation of attractors and invariant measures","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"first_name":"Oliver","full_name":"Junge, Oliver","last_name":"Junge"}],"date_created":"2020-04-15T08:33:03Z","date_updated":"2022-01-06T06:52:52Z","status":"public","type":"journal_article","publication":"Computing and Visualization in Science","language":[{"iso":"eng"}],"user_id":"15701","department":[{"_id":"101"}],"_id":"16536"},{"language":[{"iso":"eng"}],"department":[{"_id":"101"}],"user_id":"15701","_id":"16535","status":"public","abstract":[{"lang":"eng","text":"<jats:p> Recently multilevel subdivision techniques have been introduced in the numerical investigation of complicated dynamical behavior. We illustrate the applicability and efficiency of these methods by a detailed numerical study of Chua's circuit. In particular we will show that there exist two regions in phase space which are almost invariant in the sense that typical trajectories stay inside each of these sets on average for quite a long time. </jats:p>"}],"publication":"International Journal of Bifurcation and Chaos","type":"journal_article","doi":"10.1142/s0218127497001655","title":"Almost Invariant Sets in Chua's Circuit","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Junge","full_name":"Junge, Oliver","first_name":"Oliver"}],"date_created":"2020-04-15T08:31:50Z","date_updated":"2022-01-06T06:52:52Z","page":"2475-2485","citation":{"short":"M. Dellnitz, O. Junge, International Journal of Bifurcation and Chaos (1997) 2475–2485.","bibtex":"@article{Dellnitz_Junge_1997, title={Almost Invariant Sets in Chua’s Circuit}, DOI={<a href=\"https://doi.org/10.1142/s0218127497001655\">10.1142/s0218127497001655</a>}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Junge, Oliver}, year={1997}, pages={2475–2485} }","mla":"Dellnitz, Michael, and Oliver Junge. “Almost Invariant Sets in Chua’s Circuit.” <i>International Journal of Bifurcation and Chaos</i>, 1997, pp. 2475–85, doi:<a href=\"https://doi.org/10.1142/s0218127497001655\">10.1142/s0218127497001655</a>.","apa":"Dellnitz, M., &#38; Junge, O. (1997). Almost Invariant Sets in Chua’s Circuit. <i>International Journal of Bifurcation and Chaos</i>, 2475–2485. <a href=\"https://doi.org/10.1142/s0218127497001655\">https://doi.org/10.1142/s0218127497001655</a>","ama":"Dellnitz M, Junge O. Almost Invariant Sets in Chua’s Circuit. <i>International Journal of Bifurcation and Chaos</i>. 1997:2475-2485. doi:<a href=\"https://doi.org/10.1142/s0218127497001655\">10.1142/s0218127497001655</a>","chicago":"Dellnitz, Michael, and Oliver Junge. “Almost Invariant Sets in Chua’s Circuit.” <i>International Journal of Bifurcation and Chaos</i>, 1997, 2475–85. <a href=\"https://doi.org/10.1142/s0218127497001655\">https://doi.org/10.1142/s0218127497001655</a>.","ieee":"M. Dellnitz and O. Junge, “Almost Invariant Sets in Chua’s Circuit,” <i>International Journal of Bifurcation and Chaos</i>, pp. 2475–2485, 1997."},"year":"1997","publication_identifier":{"issn":["0218-1274","1793-6551"]},"publication_status":"published"},{"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science","type":"journal_article","status":"public","department":[{"_id":"101"}],"user_id":"15701","_id":"16552","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1054-1500","1089-7682"]},"publication_status":"published","page":"221-228","citation":{"bibtex":"@article{Dellnitz_Hohmann_Junge_Rumpf_1997, title={Exploring invariant sets and invariant measures}, DOI={<a href=\"https://doi.org/10.1063/1.166223\">10.1063/1.166223</a>}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, author={Dellnitz, Michael and Hohmann, Andreas and Junge, Oliver and Rumpf, Martin}, year={1997}, pages={221–228} }","short":"M. Dellnitz, A. Hohmann, O. Junge, M. Rumpf, Chaos: An Interdisciplinary Journal of Nonlinear Science (1997) 221–228.","mla":"Dellnitz, Michael, et al. “Exploring Invariant Sets and Invariant Measures.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, 1997, pp. 221–28, doi:<a href=\"https://doi.org/10.1063/1.166223\">10.1063/1.166223</a>.","apa":"Dellnitz, M., Hohmann, A., Junge, O., &#38; Rumpf, M. (1997). Exploring invariant sets and invariant measures. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, 221–228. <a href=\"https://doi.org/10.1063/1.166223\">https://doi.org/10.1063/1.166223</a>","ama":"Dellnitz M, Hohmann A, Junge O, Rumpf M. Exploring invariant sets and invariant measures. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>. 1997:221-228. doi:<a href=\"https://doi.org/10.1063/1.166223\">10.1063/1.166223</a>","chicago":"Dellnitz, Michael, Andreas Hohmann, Oliver Junge, and Martin Rumpf. “Exploring Invariant Sets and Invariant Measures.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, 1997, 221–28. <a href=\"https://doi.org/10.1063/1.166223\">https://doi.org/10.1063/1.166223</a>.","ieee":"M. Dellnitz, A. Hohmann, O. Junge, and M. Rumpf, “Exploring invariant sets and invariant measures,” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, pp. 221–228, 1997."},"year":"1997","date_created":"2020-04-15T09:06:28Z","author":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"first_name":"Andreas","full_name":"Hohmann, Andreas","last_name":"Hohmann"},{"last_name":"Junge","full_name":"Junge, Oliver","first_name":"Oliver"},{"last_name":"Rumpf","full_name":"Rumpf, Martin","first_name":"Martin"}],"date_updated":"2022-01-06T06:52:52Z","doi":"10.1063/1.166223","title":"Exploring invariant sets and invariant measures"},{"date_updated":"2022-01-06T06:52:53Z","author":[{"first_name":"Rabbijah","last_name":"Guder","full_name":"Guder, Rabbijah"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"last_name":"Kreuzer","full_name":"Kreuzer, Edwin","first_name":"Edwin"}],"date_created":"2020-04-16T08:05:37Z","title":"An adaptive method for the approximation of the generalized cell mapping","doi":"10.1016/s0960-0779(96)00118-x","publication_identifier":{"issn":["0960-0779"]},"publication_status":"published","year":"1997","page":"525-534","citation":{"chicago":"Guder, Rabbijah, Michael Dellnitz, and Edwin Kreuzer. “An Adaptive Method for the Approximation of the Generalized Cell Mapping.” <i>Chaos, Solitons &#38; Fractals</i>, 1997, 525–34. <a href=\"https://doi.org/10.1016/s0960-0779(96)00118-x\">https://doi.org/10.1016/s0960-0779(96)00118-x</a>.","ieee":"R. Guder, M. Dellnitz, and E. Kreuzer, “An adaptive method for the approximation of the generalized cell mapping,” <i>Chaos, Solitons &#38; Fractals</i>, pp. 525–534, 1997.","ama":"Guder R, Dellnitz M, Kreuzer E. An adaptive method for the approximation of the generalized cell mapping. <i>Chaos, Solitons &#38; Fractals</i>. 1997:525-534. doi:<a href=\"https://doi.org/10.1016/s0960-0779(96)00118-x\">10.1016/s0960-0779(96)00118-x</a>","apa":"Guder, R., Dellnitz, M., &#38; Kreuzer, E. (1997). An adaptive method for the approximation of the generalized cell mapping. <i>Chaos, Solitons &#38; Fractals</i>, 525–534. <a href=\"https://doi.org/10.1016/s0960-0779(96)00118-x\">https://doi.org/10.1016/s0960-0779(96)00118-x</a>","short":"R. Guder, M. Dellnitz, E. Kreuzer, Chaos, Solitons &#38; Fractals (1997) 525–534.","bibtex":"@article{Guder_Dellnitz_Kreuzer_1997, title={An adaptive method for the approximation of the generalized cell mapping}, DOI={<a href=\"https://doi.org/10.1016/s0960-0779(96)00118-x\">10.1016/s0960-0779(96)00118-x</a>}, journal={Chaos, Solitons &#38; Fractals}, author={Guder, Rabbijah and Dellnitz, Michael and Kreuzer, Edwin}, year={1997}, pages={525–534} }","mla":"Guder, Rabbijah, et al. “An Adaptive Method for the Approximation of the Generalized Cell Mapping.” <i>Chaos, Solitons &#38; Fractals</i>, 1997, pp. 525–34, doi:<a href=\"https://doi.org/10.1016/s0960-0779(96)00118-x\">10.1016/s0960-0779(96)00118-x</a>."},"_id":"16614","department":[{"_id":"101"}],"user_id":"15701","language":[{"iso":"eng"}],"publication":"Chaos, Solitons & Fractals","type":"journal_article","status":"public"},{"volume":75,"author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"last_name":"Hohmann","full_name":"Hohmann, Andreas","first_name":"Andreas"}],"date_created":"2020-05-19T09:07:27Z","date_updated":"2022-01-06T06:53:02Z","doi":"10.1007/s002110050240","title":"A subdivision algorithm for the computation of unstable manifolds and global attractors","publication_identifier":{"issn":["0029-599X","0945-3245"]},"publication_status":"published","page":"293-317","intvolume":"        75","citation":{"ama":"Dellnitz M, Hohmann A. A subdivision algorithm for the computation of unstable manifolds and global attractors. <i>Numerische Mathematik</i>. 1997;75:293-317. doi:<a href=\"https://doi.org/10.1007/s002110050240\">10.1007/s002110050240</a>","chicago":"Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the Computation of Unstable Manifolds and Global Attractors.” <i>Numerische Mathematik</i> 75 (1997): 293–317. <a href=\"https://doi.org/10.1007/s002110050240\">https://doi.org/10.1007/s002110050240</a>.","ieee":"M. Dellnitz and A. Hohmann, “A subdivision algorithm for the computation of unstable manifolds and global attractors,” <i>Numerische Mathematik</i>, vol. 75, pp. 293–317, 1997.","mla":"Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the Computation of Unstable Manifolds and Global Attractors.” <i>Numerische Mathematik</i>, vol. 75, 1997, pp. 293–317, doi:<a href=\"https://doi.org/10.1007/s002110050240\">10.1007/s002110050240</a>.","short":"M. Dellnitz, A. Hohmann, Numerische Mathematik 75 (1997) 293–317.","bibtex":"@article{Dellnitz_Hohmann_1997, title={A subdivision algorithm for the computation of unstable manifolds and global attractors}, volume={75}, DOI={<a href=\"https://doi.org/10.1007/s002110050240\">10.1007/s002110050240</a>}, journal={Numerische Mathematik}, author={Dellnitz, Michael and Hohmann, Andreas}, year={1997}, pages={293–317} }","apa":"Dellnitz, M., &#38; Hohmann, A. (1997). A subdivision algorithm for the computation of unstable manifolds and global attractors. <i>Numerische Mathematik</i>, <i>75</i>, 293–317. <a href=\"https://doi.org/10.1007/s002110050240\">https://doi.org/10.1007/s002110050240</a>"},"year":"1997","department":[{"_id":"101"}],"user_id":"32643","_id":"17015","language":[{"iso":"eng"}],"publication":"Numerische Mathematik","type":"journal_article","status":"public"},{"language":[{"iso":"eng"}],"department":[{"_id":"101"}],"user_id":"15701","_id":"16533","status":"public","publication":"Nonlinear Dynamical Systems and Chaos","type":"book_chapter","doi":"10.1007/978-3-0348-7518-9_21","title":"The Computation of Unstable Manifolds Using Subdivision and Continuation","date_created":"2020-04-15T08:27:35Z","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"first_name":"Andreas","last_name":"Hohmann","full_name":"Hohmann, Andreas"}],"date_updated":"2022-01-06T06:52:52Z","citation":{"apa":"Dellnitz, M., &#38; Hohmann, A. (1996). The Computation of Unstable Manifolds Using Subdivision and Continuation. In <i>Nonlinear Dynamical Systems and Chaos</i>. Basel. <a href=\"https://doi.org/10.1007/978-3-0348-7518-9_21\">https://doi.org/10.1007/978-3-0348-7518-9_21</a>","short":"M. Dellnitz, A. Hohmann, in: Nonlinear Dynamical Systems and Chaos, Basel, 1996.","mla":"Dellnitz, Michael, and Andreas Hohmann. “The Computation of Unstable Manifolds Using Subdivision and Continuation.” <i>Nonlinear Dynamical Systems and Chaos</i>, 1996, doi:<a href=\"https://doi.org/10.1007/978-3-0348-7518-9_21\">10.1007/978-3-0348-7518-9_21</a>.","bibtex":"@inbook{Dellnitz_Hohmann_1996, place={Basel}, title={The Computation of Unstable Manifolds Using Subdivision and Continuation}, DOI={<a href=\"https://doi.org/10.1007/978-3-0348-7518-9_21\">10.1007/978-3-0348-7518-9_21</a>}, booktitle={Nonlinear Dynamical Systems and Chaos}, author={Dellnitz, Michael and Hohmann, Andreas}, year={1996} }","ama":"Dellnitz M, Hohmann A. The Computation of Unstable Manifolds Using Subdivision and Continuation. In: <i>Nonlinear Dynamical Systems and Chaos</i>. Basel; 1996. doi:<a href=\"https://doi.org/10.1007/978-3-0348-7518-9_21\">10.1007/978-3-0348-7518-9_21</a>","ieee":"M. Dellnitz and A. Hohmann, “The Computation of Unstable Manifolds Using Subdivision and Continuation,” in <i>Nonlinear Dynamical Systems and Chaos</i>, Basel, 1996.","chicago":"Dellnitz, Michael, and Andreas Hohmann. “The Computation of Unstable Manifolds Using Subdivision and Continuation.” In <i>Nonlinear Dynamical Systems and Chaos</i>. Basel, 1996. <a href=\"https://doi.org/10.1007/978-3-0348-7518-9_21\">https://doi.org/10.1007/978-3-0348-7518-9_21</a>."},"place":"Basel","year":"1996","publication_identifier":{"isbn":["9783034875202","9783034875189"]},"publication_status":"published"},{"type":"journal_article","publication":"International Journal of Bifurcation and Chaos","status":"public","abstract":[{"lang":"eng","text":"<jats:p> In an array of coupled oscillators, synchronous chaos may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries, and this leads to the idea of symmetry breaking bifurcations of chaotic attractors. Finally, the results and ideas are illustrated for several systems of coupled oscillators. </jats:p>"}],"user_id":"15701","department":[{"_id":"101"}],"_id":"16510","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0218-1274","1793-6551"]},"citation":{"ieee":"P. J. Aston and M. Dellnitz, “Symmetry Breaking Bifurcations of Chaotic Attractors,” <i>International Journal of Bifurcation and Chaos</i>, pp. 1643–1676, 1995.","chicago":"Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations of Chaotic Attractors.” <i>International Journal of Bifurcation and Chaos</i>, 1995, 1643–76. <a href=\"https://doi.org/10.1142/s021812749500123x\">https://doi.org/10.1142/s021812749500123x</a>.","ama":"Aston PJ, Dellnitz M. Symmetry Breaking Bifurcations of Chaotic Attractors. <i>International Journal of Bifurcation and Chaos</i>. 1995:1643-1676. doi:<a href=\"https://doi.org/10.1142/s021812749500123x\">10.1142/s021812749500123x</a>","bibtex":"@article{Aston_Dellnitz_1995, title={Symmetry Breaking Bifurcations of Chaotic Attractors}, DOI={<a href=\"https://doi.org/10.1142/s021812749500123x\">10.1142/s021812749500123x</a>}, journal={International Journal of Bifurcation and Chaos}, author={Aston, Philip J. and Dellnitz, Michael}, year={1995}, pages={1643–1676} }","mla":"Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations of Chaotic Attractors.” <i>International Journal of Bifurcation and Chaos</i>, 1995, pp. 1643–76, doi:<a href=\"https://doi.org/10.1142/s021812749500123x\">10.1142/s021812749500123x</a>.","short":"P.J. Aston, M. Dellnitz, International Journal of Bifurcation and Chaos (1995) 1643–1676.","apa":"Aston, P. J., &#38; Dellnitz, M. (1995). Symmetry Breaking Bifurcations of Chaotic Attractors. <i>International Journal of Bifurcation and Chaos</i>, 1643–1676. <a href=\"https://doi.org/10.1142/s021812749500123x\">https://doi.org/10.1142/s021812749500123x</a>"},"page":"1643-1676","year":"1995","date_created":"2020-04-15T07:23:50Z","author":[{"full_name":"Aston, Philip J.","last_name":"Aston","first_name":"Philip J."},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"date_updated":"2022-01-06T06:52:52Z","doi":"10.1142/s021812749500123x","title":"Symmetry Breaking Bifurcations of Chaotic Attractors"},{"language":[{"iso":"eng"}],"_id":"16532","department":[{"_id":"101"}],"user_id":"15701","status":"public","publication":"Nonlinearity","type":"journal_article","title":"Admissible symmetry increasing bifurcations","doi":"10.1088/0951-7715/8/6/009","date_updated":"2022-01-06T06:52:52Z","date_created":"2020-04-15T08:25:12Z","author":[{"first_name":"M","last_name":"Dellnitz","full_name":"Dellnitz, M"},{"first_name":"C","last_name":"Heinrich","full_name":"Heinrich, C"}],"year":"1995","page":"1039-1066","citation":{"short":"M. Dellnitz, C. Heinrich, Nonlinearity (1995) 1039–1066.","mla":"Dellnitz, M., and C. Heinrich. “Admissible Symmetry Increasing Bifurcations.” <i>Nonlinearity</i>, 1995, pp. 1039–66, doi:<a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">10.1088/0951-7715/8/6/009</a>.","bibtex":"@article{Dellnitz_Heinrich_1995, title={Admissible symmetry increasing bifurcations}, DOI={<a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">10.1088/0951-7715/8/6/009</a>}, journal={Nonlinearity}, author={Dellnitz, M and Heinrich, C}, year={1995}, pages={1039–1066} }","apa":"Dellnitz, M., &#38; Heinrich, C. (1995). Admissible symmetry increasing bifurcations. <i>Nonlinearity</i>, 1039–1066. <a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">https://doi.org/10.1088/0951-7715/8/6/009</a>","ama":"Dellnitz M, Heinrich C. Admissible symmetry increasing bifurcations. <i>Nonlinearity</i>. 1995:1039-1066. doi:<a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">10.1088/0951-7715/8/6/009</a>","chicago":"Dellnitz, M, and C Heinrich. “Admissible Symmetry Increasing Bifurcations.” <i>Nonlinearity</i>, 1995, 1039–66. <a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">https://doi.org/10.1088/0951-7715/8/6/009</a>.","ieee":"M. Dellnitz and C. Heinrich, “Admissible symmetry increasing bifurcations,” <i>Nonlinearity</i>, pp. 1039–1066, 1995."},"publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published"},{"status":"public","publication":"Nonlinearity","type":"journal_article","language":[{"iso":"eng"}],"_id":"16542","department":[{"_id":"101"}],"user_id":"15701","year":"1995","page":"1067-1075","citation":{"apa":"Dellnitz, M., &#38; Melbourne, I. (1995). A note on the shadowing lemma and symmetric periodic points. <i>Nonlinearity</i>, 1067–1075. <a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">https://doi.org/10.1088/0951-7715/8/6/010</a>","short":"M. Dellnitz, I. Melbourne, Nonlinearity (1995) 1067–1075.","mla":"Dellnitz, M., and I. Melbourne. “A Note on the Shadowing Lemma and Symmetric Periodic Points.” <i>Nonlinearity</i>, 1995, pp. 1067–75, doi:<a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">10.1088/0951-7715/8/6/010</a>.","bibtex":"@article{Dellnitz_Melbourne_1995, title={A note on the shadowing lemma and symmetric periodic points}, DOI={<a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">10.1088/0951-7715/8/6/010</a>}, journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I}, year={1995}, pages={1067–1075} }","chicago":"Dellnitz, M, and I Melbourne. “A Note on the Shadowing Lemma and Symmetric Periodic Points.” <i>Nonlinearity</i>, 1995, 1067–75. <a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">https://doi.org/10.1088/0951-7715/8/6/010</a>.","ieee":"M. Dellnitz and I. Melbourne, “A note on the shadowing lemma and symmetric periodic points,” <i>Nonlinearity</i>, pp. 1067–1075, 1995.","ama":"Dellnitz M, Melbourne I. A note on the shadowing lemma and symmetric periodic points. <i>Nonlinearity</i>. 1995:1067-1075. doi:<a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">10.1088/0951-7715/8/6/010</a>"},"publication_identifier":{"issn":["0951-7715","1361-6544"]},"publication_status":"published","title":"A note on the shadowing lemma and symmetric periodic points","doi":"10.1088/0951-7715/8/6/010","date_updated":"2022-01-06T06:52:52Z","date_created":"2020-04-15T08:46:30Z","author":[{"first_name":"M","full_name":"Dellnitz, M","last_name":"Dellnitz"},{"first_name":"I","last_name":"Melbourne","full_name":"Melbourne, I"}]},{"type":"journal_article","publication":"International Journal of Bifurcation and Chaos","status":"public","user_id":"15701","department":[{"_id":"101"}],"_id":"16550","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0218-1274","1793-6551"]},"citation":{"chicago":"Dellnitz, Michael, Michael Field, Martin Golubitsky, Jun Ma, and Andreas Hohmann. “Cycling Chaos.” <i>International Journal of Bifurcation and Chaos</i>, 1995, 1243–47. <a href=\"https://doi.org/10.1142/s0218127495000909\">https://doi.org/10.1142/s0218127495000909</a>.","ieee":"M. Dellnitz, M. Field, M. Golubitsky, J. Ma, and A. Hohmann, “Cycling Chaos,” <i>International Journal of Bifurcation and Chaos</i>, pp. 1243–1247, 1995.","ama":"Dellnitz M, Field M, Golubitsky M, Ma J, Hohmann A. Cycling Chaos. <i>International Journal of Bifurcation and Chaos</i>. 1995:1243-1247. doi:<a href=\"https://doi.org/10.1142/s0218127495000909\">10.1142/s0218127495000909</a>","bibtex":"@article{Dellnitz_Field_Golubitsky_Ma_Hohmann_1995, title={Cycling Chaos}, DOI={<a href=\"https://doi.org/10.1142/s0218127495000909\">10.1142/s0218127495000909</a>}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Field, Michael and Golubitsky, Martin and Ma, Jun and Hohmann, Andreas}, year={1995}, pages={1243–1247} }","mla":"Dellnitz, Michael, et al. “Cycling Chaos.” <i>International Journal of Bifurcation and Chaos</i>, 1995, pp. 1243–47, doi:<a href=\"https://doi.org/10.1142/s0218127495000909\">10.1142/s0218127495000909</a>.","short":"M. Dellnitz, M. Field, M. Golubitsky, J. Ma, A. Hohmann, International Journal of Bifurcation and Chaos (1995) 1243–1247.","apa":"Dellnitz, M., Field, M., Golubitsky, M., Ma, J., &#38; Hohmann, A. (1995). Cycling Chaos. <i>International Journal of Bifurcation and Chaos</i>, 1243–1247. <a href=\"https://doi.org/10.1142/s0218127495000909\">https://doi.org/10.1142/s0218127495000909</a>"},"page":"1243-1247","year":"1995","date_created":"2020-04-15T09:04:16Z","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"first_name":"Michael","full_name":"Field, Michael","last_name":"Field"},{"full_name":"Golubitsky, Martin","last_name":"Golubitsky","first_name":"Martin"},{"first_name":"Jun","full_name":"Ma, Jun","last_name":"Ma"},{"last_name":"Hohmann","full_name":"Hohmann, Andreas","first_name":"Andreas"}],"date_updated":"2022-01-06T06:52:52Z","doi":"10.1142/s0218127495000909","title":"Cycling Chaos"},{"author":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"full_name":"Golubitsky, Martin","last_name":"Golubitsky","first_name":"Martin"},{"first_name":"Andreas","full_name":"Hohmann, Andreas","last_name":"Hohmann"},{"first_name":"Ian","last_name":"Stewart","full_name":"Stewart, Ian"}],"date_created":"2020-04-15T09:05:30Z","date_updated":"2022-01-06T06:52:52Z","doi":"10.1142/s0218127495001149","title":"Spirals in Scalar Reaction–Diffusion Equations","publication_status":"published","publication_identifier":{"issn":["0218-1274","1793-6551"]},"citation":{"chicago":"Dellnitz, Michael, Martin Golubitsky, Andreas Hohmann, and Ian Stewart. “Spirals in Scalar Reaction–Diffusion Equations.” <i>International Journal of Bifurcation and Chaos</i>, 1995, 1487–1501. <a href=\"https://doi.org/10.1142/s0218127495001149\">https://doi.org/10.1142/s0218127495001149</a>.","ieee":"M. Dellnitz, M. Golubitsky, A. Hohmann, and I. Stewart, “Spirals in Scalar Reaction–Diffusion Equations,” <i>International Journal of Bifurcation and Chaos</i>, pp. 1487–1501, 1995.","ama":"Dellnitz M, Golubitsky M, Hohmann A, Stewart I. Spirals in Scalar Reaction–Diffusion Equations. <i>International Journal of Bifurcation and Chaos</i>. 1995:1487-1501. doi:<a href=\"https://doi.org/10.1142/s0218127495001149\">10.1142/s0218127495001149</a>","apa":"Dellnitz, M., Golubitsky, M., Hohmann, A., &#38; Stewart, I. (1995). Spirals in Scalar Reaction–Diffusion Equations. <i>International Journal of Bifurcation and Chaos</i>, 1487–1501. <a href=\"https://doi.org/10.1142/s0218127495001149\">https://doi.org/10.1142/s0218127495001149</a>","short":"M. Dellnitz, M. Golubitsky, A. Hohmann, I. Stewart, International Journal of Bifurcation and Chaos (1995) 1487–1501.","bibtex":"@article{Dellnitz_Golubitsky_Hohmann_Stewart_1995, title={Spirals in Scalar Reaction–Diffusion Equations}, DOI={<a href=\"https://doi.org/10.1142/s0218127495001149\">10.1142/s0218127495001149</a>}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}, year={1995}, pages={1487–1501} }","mla":"Dellnitz, Michael, et al. “Spirals in Scalar Reaction–Diffusion Equations.” <i>International Journal of Bifurcation and Chaos</i>, 1995, pp. 1487–501, doi:<a href=\"https://doi.org/10.1142/s0218127495001149\">10.1142/s0218127495001149</a>."},"page":"1487-1501","year":"1995","user_id":"15701","department":[{"_id":"101"}],"_id":"16551","language":[{"iso":"eng"}],"type":"journal_article","publication":"International Journal of Bifurcation and Chaos","status":"public","abstract":[{"lang":"eng","text":"<jats:p> Spiral patterns have been observed experimentally, numerically, and theoretically in a variety of systems. It is often believed that these spiral wave patterns can occur only in systems of reaction–diffusion equations. We show, both theoretically (using Hopf bifurcation techniques) and numerically (using both direct simulation and continuation of rotating waves) that spiral wave patterns can appear in a single reaction–diffusion equation [ in u(x, t)] on a disk, if one assumes \"spiral\" boundary conditions (u<jats:sub>r</jats:sub> = mu<jats:sub>θ</jats:sub>). Spiral boundary conditions are motivated by assuming that a solution is infinitesimally an Archimedian spiral near the boundary. It follows from a bifurcation analysis that for this form of spirals there are no singularities in the spiral pattern (technically there is no spiral tip) and that at bifurcation there is a steep gradient between the \"red\" and \"blue\" arms of the spiral. </jats:p>"}]}]