{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:31:43Z","timestamp":1760783503944},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,2,10]],"date-time":"2012-02-10T00:00:00Z","timestamp":1328832000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2012,8]]},"DOI":"10.1007\/s00034-012-9392-3","type":"journal-article","created":{"date-parts":[[2012,2,9]],"date-time":"2012-02-09T15:46:09Z","timestamp":1328802369000},"page":"1279-1296","source":"Crossref","is-referenced-by-count":20,"title":["Circuits with Oscillatory Hierarchical Farey Sequences and Fractal Properties"],"prefix":"10.1007","volume":"31","author":[{"given":"Wieslaw","family":"Marszalek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,2,10]]},"reference":[{"key":"9392_CR1","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1137\/S0895479800378660","volume":"24","author":"R.E. Beardmore","year":"2002","unstructured":"R.E. Beardmore, R. Laister, The flow of a differential-algebraic equation near a singular equilibrium. SIAM J. Matrix Anal. 24, 106\u2013120 (2002)","journal-title":"SIAM J. Matrix Anal."},{"key":"9392_CR2","first-page":"39","volume":"49","author":"M. Br\u00f8ns","year":"2006","unstructured":"M. Br\u00f8ns, M. Krupa, M. Wechselberger, Mixed mode oscillations due to the generalized canard phenomenon. Fields Inst. Commun. 49, 39\u201363 (2006)","journal-title":"Fields Inst. Commun."},{"key":"9392_CR3","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.physd.2004.10.006","volume":"200","author":"K.E. Chlouverakis","year":"2005","unstructured":"K.E. Chlouverakis, J.C. Sprott, A comparison of correlation and Lyapunov dimensions. Physica D 200, 156\u2013164 (2005)","journal-title":"Physica D"},{"key":"9392_CR4","first-page":"H1315","volume":"274","author":"S. Brouwer De","year":"1998","unstructured":"S. De Brouwer, D.H. Edwards, T.M. Griffith, Simplifications of the quasiperiodic route to chaos in agonist-induced vasomotion by iterative circle maps. Am. J. Physiol. 274, H1315\u2013H1326 (1998)","journal-title":"Am. J. Physiol."},{"key":"9392_CR5","doi-asserted-by":"crossref","first-page":"7151","DOI":"10.1103\/PhysRevE.58.7151","volume":"58","author":"R. Eichhorn","year":"1998","unstructured":"R. Eichhorn, S.J. Linz, P. H\u00e4nggi, Transformations of nonlinear dynamical systems to jerky motion and its application to minimal chaotic flows. Phys. Rev. E 58, 7151\u20137164 (1998)","journal-title":"Phys. Rev. E"},{"key":"9392_CR6","doi-asserted-by":"crossref","unstructured":"Focus issue: Mixed mode oscillations: experiment, computation, and analysis. Chaos 18(1) (2008)","DOI":"10.1063\/1.2903177"},{"key":"9392_CR7","doi-asserted-by":"crossref","first-page":"586","DOI":"10.2307\/2302799","volume":"45","author":"L.R. Ford","year":"1938","unstructured":"L.R. Ford, Fractions. Am. Math. Mon. 45, 586\u2013601 (1938)","journal-title":"Am. Math. Mon."},{"key":"9392_CR8","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1016\/j.physleta.2011.01.017","volume":"375","author":"J.G. Freire","year":"2011","unstructured":"J.G. Freire, J.A.C. Gallas, Stern\u2013Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer\u2013van der Pol and FitzHugh\u2013Nagumo models of excitable systems. Phys. Lett. A 375, 1097\u20131103 (2011)","journal-title":"Phys. Lett. A"},{"key":"9392_CR9","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1137\/070688912","volume":"7","author":"M. Krupa","year":"2008","unstructured":"M. Krupa, N. Popovic, N. Kopell, Mixed-mode oscillations in three time-scale systems: a prototypical example. SIAM J. Appl. Dyn. Syst. 7, 361\u2013420 (2008)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"9392_CR10","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1006\/jdeq.2000.3929","volume":"174","author":"M. Krupa","year":"2001","unstructured":"M. Krupa, P. Szmolyan, Relaxation oscillation and canard explosion. J. Differ. Equ. 174, 312\u2013368 (2001)","journal-title":"J. Differ. Equ."},{"key":"9392_CR11","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/0375-9601(81)90165-1","volume":"86","author":"R.B. Leipnik","year":"1981","unstructured":"R.B. Leipnik, T.A. Newton, Double strange attractors in rigid body motion with linear feedback control. Phys. Lett. A 86, 63\u201367 (1981)","journal-title":"Phys. Lett. A"},{"key":"9392_CR12","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1119\/1.19052","volume":"66","author":"S.J. Linz","year":"1998","unstructured":"S.J. Linz, Newtonian jerky dynamics: some general properties. Am. J. Phys. 66, 1109\u20131114 (1998)","journal-title":"Am. J. Phys."},{"key":"9392_CR13","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1109\/TPS.2008.2006842","volume":"37","author":"W. Marszalek","year":"2009","unstructured":"W. Marszalek, Fold points and singularities in Hall MHD differential-algebraic equations. IEEE Trans. Plasma Sci. 37, 254\u2013260 (2009)","journal-title":"IEEE Trans. Plasma Sci."},{"key":"9392_CR14","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.camwa.2004.06.030","volume":"49","author":"W. Marszalek","year":"2005","unstructured":"W. Marszalek, T. Amdeberhan, R. Riaza, Singularity crossing phenomena in DAEs: a two-phase fluid flow application case study. Comput. Math. Appl. 49, 303\u2013319 (2005)","journal-title":"Comput. Math. Appl."},{"key":"9392_CR15","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1109\/TPWRS.2004.841244","volume":"20","author":"W. Marszalek","year":"2005","unstructured":"W. Marszalek, Z. Trzaska, Singularity-induced bifurcations in electrical power systems. IEEE Trans. Power Syst. 20, 312\u2013320 (2005)","journal-title":"IEEE Trans. Power Syst."},{"key":"9392_CR16","first-page":"1075","volume":"29","author":"W. Marszalek","year":"2010","unstructured":"W. Marszalek, Z. Trzaska, Mixed-mode oscillations in a modified Chua\u2019s circuit. Circuits, Systems. Signal Process. 29, 1075\u20131087 (2010)","journal-title":"Signal Process."},{"key":"9392_CR17","doi-asserted-by":"crossref","first-page":"6430","DOI":"10.1063\/1.451473","volume":"85","author":"J. Maselko","year":"1986","unstructured":"J. Maselko, L. Swinney, Complex periodic oscillations and Farey arithmetic in the Belousov\u2013Zhabotinskii reaction. J. Chem. Phys. 85, 6430\u20136441 (1986)","journal-title":"J. Chem. Phys."},{"key":"9392_CR18","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1016\/j.physleta.2011.02.028","volume":"375","author":"B. Munmuangsaen","year":"2011","unstructured":"B. Munmuangsaen, B. Srisuchinwong, J.C. Sprott, Generalization of the simplest autonomous chaotic system. Phys. Lett. A 375, 1445\u20131450 (2011)","journal-title":"Phys. Lett. A"},{"key":"9392_CR19","doi-asserted-by":"crossref","first-page":"6191","DOI":"10.1063\/1.463727","volume":"97","author":"V. Petrov","year":"1992","unstructured":"V. Petrov, S.K. Scott, K. Showalter, Mixed-mode oscillations in chemical systems. J. Chem. Phys. 97, 6191\u20136198 (1992)","journal-title":"J. Chem. Phys."},{"key":"9392_CR20","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1016\/0016-0032(94)90087-6","volume":"331B","author":"L. Pivka","year":"1994","unstructured":"L. Pivka, C.W. Wu, A. Huang, Chua\u2019s oscillator: a compendium of chaotic phenomena. J. Franklin Inst. 331B, 705\u2013741 (1994)","journal-title":"J. Franklin Inst."},{"key":"9392_CR21","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/BF01212467","volume":"19","author":"R. Riaza","year":"2000","unstructured":"R. Riaza, S.L. Campbell, W. Marszalek, On singular equilibria of index-1 DAEs. Circuits Syst. Signal Process. 19, 131\u2013157 (2000)","journal-title":"Circuits Syst. Signal Process."},{"key":"9392_CR22","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/TCSII.2011.2124490","volume":"58","author":"J.C. Sprott","year":"2011","unstructured":"J.C. Sprott, A new chaotic jerk circuits. IEEE Trans. Circuits Syst. II, Express Briefs. 58, 240\u2013243 (2011)","journal-title":"IEEE Trans. Circuits Syst. II, Express Briefs"},{"key":"9392_CR23","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1137\/030601995","volume":"4","author":"M. Wechselberger","year":"2005","unstructured":"M. Wechselberger, Existence and bifurcations of canards in R 3 in the case of a folded node. SIAM J. Appl. Dyn. Syst. 4, 101\u2013139 (2005)","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"9392_CR24","unstructured":"N.J. Wildberger, Evolution versus intelligent design: a mathematician\u2019s view. http:\/\/web.maths.unsw.edu.au\/norman\/papers\/IntelligentDesignhtml\/IntelligentDesign1.htm (2008). Accessed 19 Dec. 2011"},{"key":"9392_CR25","doi-asserted-by":"crossref","first-page":"181","DOI":"10.2528\/PIERM09021501","volume":"8","author":"X.-X. Xu","year":"2009","unstructured":"X.-X. Xu, S.-J. Ma, P.-T. Huang, New concepts in electromagnetic jerky dynamics and their applications in transient processes of electric circuit. Prog. Electromagn. Res. M. 8, 181\u2013194 (2009)","journal-title":"Prog. Electromagn. Res. M."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-012-9392-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00034-012-9392-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-012-9392-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,23]],"date-time":"2019-06-23T11:23:41Z","timestamp":1561289021000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00034-012-9392-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,10]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["9392"],"URL":"https:\/\/doi.org\/10.1007\/s00034-012-9392-3","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,10]]}}}