{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,12]],"date-time":"2026-07-12T04:11:57Z","timestamp":1783829517503,"version":"3.55.0"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T00:00:00Z","timestamp":1665360000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T00:00:00Z","timestamp":1665360000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s00500-022-07501-1","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T17:02:46Z","timestamp":1665421366000},"page":"2769-2782","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Generation of multiscroll chaotic attractors of a finance system with mirror symmetry"],"prefix":"10.1007","volume":"27","author":[{"given":"Anam","family":"Azam","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Danish Ali","family":"Sunny","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Aqeel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,10,10]]},"reference":[{"key":"7501_CR1","doi-asserted-by":"crossref","first-page":"1850049","DOI":"10.1142\/S0129183118500493","volume":"29","author":"W Ai","year":"2018","unstructured":"Ai W, Sun K, Fu Y (2018) Design of multiwing-multiscroll grid compound chaotic system and its circuit implementation. Int J Mod Phys C 29:1850049","journal-title":"Int J Mod Phys C"},{"key":"7501_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11071-017-3641-8","volume":"90","author":"A Azam","year":"2017","unstructured":"Azam A, Aqeel M, Salman A, Faizan A (2017) Chaotic behaviour of modified stretched-twist-fold flow with fractal property. Nonlinear Dyn 90:1\u201312","journal-title":"Nonlinear Dyn"},{"key":"7501_CR3","doi-asserted-by":"crossref","first-page":"2521","DOI":"10.1007\/s00500-020-05325-5","volume":"25","author":"A Azam","year":"2021","unstructured":"Azam A, Aqeel M, Hussain Z (2021) On the dynamics: existence of chaos and symmetry in Krauseand Robert (KR) flow. Soft Comput 25:2521\u20132530","journal-title":"Soft Comput"},{"key":"7501_CR4","first-page":"213","volume":"3","author":"G Cai","year":"2007","unstructured":"Cai G, Huang J (2007) A new finance chaotic attractor. Int J Nonlinear Sci 3:213\u2013220","journal-title":"Int J Nonlinear Sci"},{"key":"7501_CR5","doi-asserted-by":"crossref","first-page":"1789","DOI":"10.1142\/S0218127402005467","volume":"8","author":"S Celikovsky","year":"2002","unstructured":"Celikovsky S, Chen GR (2002) On a generalized Lorenz canonical form of chaotic system via nonlinear observed approach. Int J Bifurc Chaos 8:1789\u20131812","journal-title":"Int J Bifurc Chaos"},{"issue":"1","key":"7501_CR6","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.chaos.2004.11.044","volume":"25","author":"LD Cesare","year":"2005","unstructured":"Cesare LD, Sportelli M (2005) A dynamics IS-LM model with delayed taxation revenues. Chaos Solitons Fractals 25(1):233\u2013244","journal-title":"Chaos Solitons Fractals"},{"key":"7501_CR7","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1142\/S0218127499001024","volume":"9","author":"GR Chen","year":"1999","unstructured":"Chen GR, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9:1465\u20131466","journal-title":"Int J Bifurc Chaos"},{"key":"7501_CR8","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1049\/el:20030559","volume":"39","author":"A Elwakil","year":"2003","unstructured":"Elwakil A, Ozoguz S (2003) Chaos in a pulse-excited resonator with self-feedback. Electron Lett 39:831\u2013833","journal-title":"Electron Lett"},{"issue":"9","key":"7501_CR9","doi-asserted-by":"crossref","first-page":"862","DOI":"10.1109\/TCSII.2006.880032","volume":"53","author":"A Elwakil","year":"2006","unstructured":"Elwakil A, Ozoguz S (2006) Multiscroll chaotic oscillators: the nonautonomous approach. IEEE Trans Circuits Sys I 53(9):862\u2013866","journal-title":"IEEE Trans Circuits Sys I"},{"key":"7501_CR10","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/81.995671","volume":"49","author":"AS Elwakil","year":"2002","unstructured":"Elwakil AS, Ozoguz S, Kennedy MP (2002) Creation of a complex butterfly attractor using a novel Lorenz-type system. IEEE Trans Circuits Syst I 49:527\u2013530","journal-title":"IEEE Trans Circuits Syst I"},{"issue":"2","key":"7501_CR11","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1016\/j.chaos.2005.11.024","volume":"32","author":"L Fanti","year":"2007","unstructured":"Fanti L, Manfredi P (2007) Chaotic business cycles and fiscal policy: an IS-LM model with distributed tax collection lags. Chaos Solitons Fractals 32(2):736\u2013744","journal-title":"Chaos Solitons Fractals"},{"key":"7501_CR12","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2021.111743","volume":"155","author":"M Fiaz","year":"2022","unstructured":"Fiaz M, Aqeel M, Marwan M, Sabir M (2022) Integer and fractional order analysis of a 3D system and generalization of synchronization for a class of chaotic systems. Chaos Fractal Soliton 155:111743","journal-title":"Chaos Fractal Soliton"},{"issue":"9","key":"7501_CR13","doi-asserted-by":"crossref","first-page":"2150127","DOI":"10.1142\/S0218127421501273","volume":"31","author":"M Fiaz","year":"2021","unstructured":"Fiaz M, Aqeel M, Marwan M, Sabir M (2021) Retardational effect and hopf bifurcations in a new attitude system of quad-rotor unmanned aerial vehicle. Int J Bifurc Chaos 31(9):2150127","journal-title":"Int J Bifurc Chaos"},{"issue":"1\u20132","key":"7501_CR14","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s11071-009-9472-5","volume":"58","author":"Q Gao","year":"2009","unstructured":"Gao Q, Ma J (2009) Chaos and Hopf bifurcation of a finance system. Nonlinear Dyn 58(1\u20132):209\u2013216","journal-title":"Nonlinear Dyn"},{"key":"7501_CR15","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195310658.001.0001","volume-title":"The symmetry of chaos","author":"R Gilmore","year":"2007","unstructured":"Gilmore R, Letellier C (2007) The symmetry of chaos. Oxford University Press, Oxford"},{"issue":"1","key":"7501_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1907905","volume":"19","author":"RM Goodwin","year":"1951","unstructured":"Goodwin RM (1951) The nonlinear accelerator and the persistence of business cycles. Econometrica 19(1):1\u201317","journal-title":"Econometrica"},{"key":"7501_CR17","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1007\/s00500-013-1071-1","volume":"18","author":"F Haiyang","year":"2014","unstructured":"Haiyang F, Minqiang L, Fuzan C (2014) Chaotic dynamics in the software market with network Externalities. Soft Comput 18:509\u2013519","journal-title":"Soft Comput"},{"issue":"2016","key":"7501_CR18","first-page":"1","volume":"195","author":"L He","year":"2016","unstructured":"He L, Yi L, Tang P (2016) Numerical scheme and dynamic analysis for variable-order fractional van der Pol model of nonlinear economic cycle. Adv Differ Equ 195(2016):1\u201311","journal-title":"Adv Differ Equ"},{"issue":"8","key":"7501_CR19","doi-asserted-by":"crossref","first-page":"1480","DOI":"10.1109\/TCAD.2018.2855121","volume":"38","author":"Q Hong","year":"2018","unstructured":"Hong Q, Li Y, Wang X, Zeng Z (2018) A versatile pulse control method to generate arbitrary multidirection multibutterfly chaotic attractors. IEEE Trans Comput Aided Des Integr Circuits Syst 38(8):1480\u20131492","journal-title":"IEEE Trans Comput Aided Des Integr Circuits Syst"},{"issue":"8","key":"7501_CR20","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1063\/1.4959538","volume":"26","author":"Q Hong","year":"2016","unstructured":"Hong Q, Xie Q, Shen Y, Wang X (2016) Generating multi-double-scroll attractors via nonautonomous approach. Chaos 26(8):130\u2013141","journal-title":"Chaos"},{"issue":"2","key":"7501_CR21","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1007\/s11071-016-3094-5","volume":"87","author":"Q Hong","year":"2017","unstructured":"Hong Q, Xie Q, Xiao P (2017) A novel approach for generating multi-direction multi\u2013double-scroll attractors. Nonlinear Dyn 87(2):1015\u20131030","journal-title":"Nonlinear Dyn"},{"issue":"5","key":"7501_CR22","first-page":"496","volume":"62","author":"Y Huang","year":"2015","unstructured":"Huang Y, Zhang P, Zhao W (2015) Novel grid multiwing butterfly chaotic attractors and their circuit design. IEEE Trans Circuits Syst II Exp Briefs 62(5):496\u2013500","journal-title":"IEEE Trans Circuits Syst II Exp Briefs"},{"key":"7501_CR23","doi-asserted-by":"crossref","first-page":"12373","DOI":"10.1007\/s00500-021-05950-8","volume":"25","author":"F Jiayi","year":"2021","unstructured":"Jiayi F, Wenjing X, Yi H, Dinesh RJ (2021) Application of chaos cuckoo search algorithm in computer vision technology. Soft Comput 25:12373\u201312387","journal-title":"Soft Comput"},{"key":"7501_CR24","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1140\/epjp\/s13360-020-00316-9","volume":"135","author":"A Javeria","year":"2020","unstructured":"Javeria A, Aqeel M, Salman A, Zainab R (2020) Absolute control of chaotic responses in Robbins disc Dynamo. Eur Phys J plus 135:307","journal-title":"Eur Phys J plus"},{"key":"7501_CR25","first-page":"659","volume":"3","author":"L Jh","year":"2002","unstructured":"Jh L, Chen GR (2002) A new chaotic attractor coined. Int J Bifurc Chaos 3:659\u2013661","journal-title":"Int J Bifurc Chaos"},{"key":"7501_CR26","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","volume":"20","author":"EN Lorenz","year":"1963","unstructured":"Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130\u2013141","journal-title":"J Atmos Sci"},{"issue":"4","key":"7501_CR27","doi-asserted-by":"crossref","first-page":"2671","DOI":"10.1007\/s11071-017-3402-8","volume":"88","author":"M Siddique","year":"2017","unstructured":"Siddique M, Rehan M, Bhatti MKL, Ahmed S (2017) Delay range-dependent local adaptive and robust adaptive synchronization approaches for time-delay chaotic systems. Nonlin Dyn 88(4):2671\u20132691","journal-title":"Nonlin Dyn"},{"issue":"12","key":"7501_CR28","first-page":"1236","volume":"22","author":"J Ma","year":"2001","unstructured":"Ma J, Chen Y (2001) Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (II). Appl Math Mech 22(12):1236\u20131242","journal-title":"Appl Math Mech"},{"key":"7501_CR29","doi-asserted-by":"crossref","first-page":"4333","DOI":"10.1007\/s00500-019-04197-8","volume":"24","author":"M Marwan","year":"2020","unstructured":"Marwan M, Mehboob M, Ahmad S, Aqeel M (2020) Hopf bifurcation of forced Chen system and its stability via adaptive control with arbitrary parameters. Soft Comput 24:4333\u20134341","journal-title":"Soft Comput"},{"issue":"11","key":"7501_CR30","doi-asserted-by":"crossref","first-page":"2050220","DOI":"10.1142\/S021812742050220X","volume":"30","author":"X Peng","year":"2020","unstructured":"Peng X, Zeng Y (2020) A simple method for generating mirror symmetry composite multiscroll chaotic attractors. Int J Bifurc Chaos 30(11):2050220","journal-title":"Int J Bifurc Chaos"},{"issue":"5","key":"7501_CR31","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1016\/j.chaos.2003.12.065","volume":"21","author":"V Rai","year":"2004","unstructured":"Rai V, Upadhyay RK (2004) Chaotic population dynamics and biology of top predator. Chaos Solitons Fractals 21(5):1195\u20131204","journal-title":"Chaos Solitons Fractals"},{"key":"7501_CR32","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/0375-9601(76)90101-8","volume":"57","author":"OE Rossler","year":"1976","unstructured":"Rossler OE (1976) An equation for continuous chaos. Phys Lett A 57:397\u2013398","journal-title":"Phys Lett A"},{"issue":"3","key":"7501_CR33","first-page":"1144","volume":"219","author":"SF Al Azzawi","year":"2004","unstructured":"Al Azzawi SF (2004) Stability and bifurcation of pan chaotic system by using Routh-Hurwitz and gardan methods. Appl Math Comput 219(3):1144\u20131152","journal-title":"Appl Math Comput"},{"issue":"4","key":"7501_CR34","first-page":"3905","volume":"60","author":"EM Shahverdiev","year":"1999","unstructured":"Shahverdiev EM (1999) Boundedness of dynamical systems and chaos synchronization. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip 60(4):3905\u20133909","journal-title":"Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip"},{"key":"7501_CR35","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1103\/PhysRevE.50.R647","volume":"50","author":"JC Sprott","year":"1994","unstructured":"Sprott JC (1994) Some simple chaotic flows. Phys Rev E 50:647\u2013650","journal-title":"Phys Rev E"},{"key":"7501_CR36","first-page":"1","volume":"27","author":"C Sun","year":"2017","unstructured":"Sun C, Chen Z, Xu Q (2017) Generating a double scroll attractor by connecting a pair of mutual mirror image attractors via planar switching control. Int J Bifurc Chaos 27:1\u201316","journal-title":"Int J Bifurc Chaos"},{"issue":"4","key":"7501_CR37","doi-asserted-by":"crossref","first-page":"1550056","DOI":"10.1142\/S021812741550056X","volume":"25","author":"FR Tahir","year":"2015","unstructured":"Tahir FR, Jafari S, Pham VT, Volocs C, Wang X (2015) A novel no-equilibrium system with multiwing butterfly attractors. Int J Bifurc Chaos 25(4):1550056","journal-title":"Int J Bifurc Chaos"},{"key":"7501_CR38","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1515\/nleng-2018-0012","volume":"8","author":"S Vaidyanathan","year":"2019","unstructured":"Vaidyanathan S, Sambas A, Kacar S, Cavusoglu U (2019) A new finance chaotic system, its electronic circuit realization, passivity based synchronization and an application to voice encryption. Nonlinear Eng 8:193\u2013205","journal-title":"Nonlinear Eng"},{"issue":"1","key":"7501_CR39","first-page":"79","volume":"12","author":"A Vlad","year":"2010","unstructured":"Vlad A, Pasco P, Morariu N (2010) Chaos models in economics. J Comput 12(1):79\u201383","journal-title":"J Comput"},{"issue":"12","key":"7501_CR40","doi-asserted-by":"crossref","first-page":"4471","DOI":"10.1142\/S0218127407020130","volume":"17","author":"ME Yalcin","year":"2007","unstructured":"Yalcin ME (2007) Increasing the entropy of a random number generator using n-scroll chaotic attractors. Int J Bifurc Chaos 17(12):4471\u20134479","journal-title":"Int J Bifurc Chaos"},{"issue":"10","key":"7501_CR41","doi-asserted-by":"crossref","first-page":"2050148","DOI":"10.1142\/S0218127420501485","volume":"30","author":"T Yang","year":"2020","unstructured":"Yang T (2020) Dynamical analysis of a finance system with nonconstant elasticity of demand. Int J Bifurc Chaos 30(10):2050148","journal-title":"Int J Bifurc Chaos"},{"issue":"5","key":"7501_CR42","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1109\/TCSI.2011.2180429","volume":"59","author":"S Yu","year":"2012","unstructured":"Yu S, L\u00fc J, Yu X, Chen G (2012) Design and implementation of grid multiwing Lorenz system family via switching control and constructing super-heteroclinic loops. IEEE Trans Circuits Syst I 59(5):1015\u20131028","journal-title":"IEEE Trans Circuits Syst I"},{"key":"7501_CR43","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1002\/cta.736","volume":"41","author":"C Zhang","year":"2010","unstructured":"Zhang C, Yu S (2010) On constructing complex grid multi-wing hyperchaotic system: theoretical design and circuit implementation. Int J Circ Th Appl 41:221\u2013237","journal-title":"Int J Circ Th Appl"},{"issue":"11","key":"7501_CR44","doi-asserted-by":"crossref","first-page":"4575","DOI":"10.1016\/j.ijleo.2016.01.027","volume":"127","author":"C Zhang","year":"2016","unstructured":"Zhang C (2016) Theoretical design approach of four-dimensional piecewise linear multi-wing hyperchaotic differential dynamic system. Opt Int J Light Electron Opt 127(11):4575\u20134580","journal-title":"Opt Int J Light Electron Opt"},{"key":"7501_CR45","first-page":"1","volume":"27","author":"L Zhou","year":"2017","unstructured":"Zhou L, Wang C, Zhou L (2017) Generating four-wing hyperchaotic attractor and two-wing, three wing, and four-wing chaotic attractors in 4D memristive system. Int J Bifurc Chaos 27:1\u201314","journal-title":"Int J Bifurc Chaos"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07501-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-022-07501-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07501-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,28]],"date-time":"2023-11-28T18:12:54Z","timestamp":1701195174000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-022-07501-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,10]]},"references-count":45,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["7501"],"URL":"https:\/\/doi.org\/10.1007\/s00500-022-07501-1","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,10]]},"assertion":[{"value":"6 September 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}