Abstract
A new three-dimensional continuous autonomous system is proposed in this paper and it exhibits single scroll chaotic behavior in a particular parameter region. By linear stability analysis and numerical simulations, we investigate different dynamical observations with respect to system parameters and try to understand the route to generation of chaos. For a large portion of the parameter region, we see a sudden birth of a period-three limit cycle. Then the period-three orbit turns into a chaotic state through typical Pomeau-Manneville intermittent route to chaos. Lyapunov exponent and Kaplan-Yorke dimension are used to verify the chaotic behavior. It becomes periodic via inverse period-doubling route for higher values of the parameters. A two-parameter bifurcation diagram is shown which distinguishes the chaotic region from other periodic and steady-state regions.
Similar content being viewed by others
References
S. Strogatz, Nonlinear dynamics and chaos (Westview Press, USA, 2014)
E. Ott, Chaos in dynamical system (Cambridge University Press, UK, 2002)
J. Wang, W. Jiang, Nonlinear Dyn. 69, 1541 (2012)
J. Ginoux, R. Naeck, Y.B. Ruhomally, M.Z. Dauhoo, M. Perc, Appl. Math. Comput. 347, 502 (2019)
D. Ghosh, A.R. Chowdhury, J. Comput. Nonlinear Dyn. 2, 267 (2007)
D. Guégan, Annu. Rev. Control 33, 89 (2009)
S. Kodba, M. Perc, M. Marhl, Eur. J. Phys. 26, 205 (2005)
C. Sparrow, The Lorenz equations: bifurcations, chaos, and strange attractors (Springer Science & Business Media, 2012)
B. Wang, S. Zhou, X. Zheng, C. Zhou, J. Dong, J. Zhao, Optik 126, 4846 (2015)
S. Çiçek, A. Ferikoğlu, I. Pehlivan, Optik 127, 4024 (2016)
C.K. Volos, I.M. Kyprianidis, I.N. Stouboulos, Rob. Auton. Syst. 60, 651 (2012)
M. Virte, E. Mercier, H. Thienpont, K. Panajotov, M. Sciamanna, Opt. Express. 22, 17271 (2014)
E.M. Shahverdiev, K.A. Shore, Optik 124, 1350 (2013)
M.A. Budroni, I. Calabrese, Y. Miele, M. Rustici, N. Marchettini, F. Rossi, Phys. Chem. Chem. Phys. 19, 32235 (2017)
M.Y. Parvees, J.A. Samath, I.K. Raj, R.M. Nirmal, J. Med. Imaging Health Inf. 7, 118 (2017)
S. Banerjee, D. Ghosh, A. Ray, A. Roy Chowdhury, Europhys. Lett. 81, 20006 (2007)
D. Ghosh, S. Banerjee, A. Roy Chowdhury, Europhys. Lett. 80, 30006 (2007)
S. Banerjee, D. Ghosh, A. Roy Chowdhury, Phys. Scr. 78, 015010 (2008)
S. Vaidyanathan, A. Sambas, M. Mamat, Int. J. Model. Identif. Control. 28, 153 (2017)
J.M. Ginoux, H. Ruskeepää, M. Perc, R. Naeck, V. Di Costanzo, M. Bouchouicha, F. Fnaiech, M. Sayadi, T. Hamdi, Chaos Solitons Fractals 111, 198 (2018)
A. Ray, D. Ghosh, A.R. Chowdhury, Phys. Lett. A 372, 5329 (2008)
E. Lorenz, J. Atmos. Sci. 20, 130 (1963)
E.O. Rössler, Phys. Lett. A 57, 397 (1976)
R.M. May, Nature 261, 459 (1976)
J.L. Hindmarsh, R.M. Rose, Proc. R. Soc. London B 221, 87 (1984)
L.O. Chua, M. Komuro, IEEE Trans. Circuits Syst. 32, 797 (1985)
G.R. Chen, T. Ueta, Int. J. Bifurc. Chaos 9, 1465 (1999)
J.C. Sprott, Phys. Rev. E 50, R647 (1994)
J.C. Sprott, Phys. Lett. A 266, 19 (2000)
J. Lü, G. Chen, Int. J. Bifurc. Chaos 12, 1789 (2002)
P.H.O. Silva, L.G. Nerdo, S.A.M. Martins, E.G. Nepomuceno, M. Perc, Eur. J. Phys. 39, 065105 (2018)
M. Perc, Eur. J. Phys. 26, 579 (2005)
S.N. Chowdhury, S. Majhi, D. Ghosh, A. Prasad, Phys. Lett. A 383, 125997 (2019)
A. Bayani, K. Rajagopal, A.J.M. Khalaf, S. Jafari, G.D. Leutcho, J. Kengne, Phys. Lett. A 383, 1450 (2019)
A. Ray, D. Ghosh, A.R. Chowdhury, J. Phys. A 42, 385102 (2009)
D. Dudkowski, S. Jafari, T. Kapitaniak, N.V. Kuznestov, G.A. Leonov, A. Prasad, Phys. Rep. 637, 1 (2016)
Z. Wei, Phys. Lett. A 376, 102 (2011)
S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, Phys. Lett. A 377, 699 (2013)
M. Molaiei, S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, Int. J. Bifurc. Chaos 23, 1350188 (2013)
S. Jafari, J.C. Sprott, Chaos Solitons Fractals 57, 79 (2013)
S. Jafari, J.C. Sprott, V.T. Pham, C. Volos, C. Li, Nonlinear Dyn. 86, 1349 (2016)
D. Ghosh, S. Khajanchi, S. Mangiarotti, F. Denis, S.K. Dana, C. Letellier, BioSystems 158, 17 (2017)
S. Khajanchi, M. Perc, D. Ghosh, Chaos 28, 103101 (2018)
E. Ott, C. Grebogi, J.A. Yorke, Phys. Rev. Lett. 64, 1196 (1990)
S. Boccaletti, C. Grebogi, Y.C. Lai, H. Mancini, D. Maza, Phys. Rep. 329, 103 (2000)
M. Jun, W. Qing-Yun, J. Wu-Yin, X. Ya-Feng, Chin. Phys. Lett. 25, 3582 (2008)
S. Boccaletti, C. Grebogi, Y.C. Li, H. Mancini, D. Maza, Phys. Rep. 329, 103 (2000)
D. Ghosh, A.R. Chowdhury, P. Saha, Chaos Solitons Fractals 35, 472 (2008)
S.K. Bhowmick, D. Ghosh, P. Roy, S.K. Dana, K. Murali, S. Sinha, Int. J. Bifurc. Chaos 24, 1450014 (2014)
A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)
P. Grassberger, I. Procaccia, Physica D 9, 189 (1983)
C. Liu, T. Liu, L. Liu, K. Liu, Chaos Solitons Fractals 22, 1031 (2004)
X. Wang, G. Chen, Commun. Nonlinear Sci. Numer. Simul. 17, 1264 (2012)
A. Ray, D. Ghosh, Int. J. Bifurc. Chaos (to be published)
A. Dhooge, W. Govaerts, Y.A. Kuznetsov, ACS Trans. Math. Software 29, 141 (2003)
Y.A. Kuznetsov, Elements of applied bifurcation theory (Springer, USA, 2004)
Y. Pomeau, P. Manneville, Commun. Math. Phys. 74, 189 (1980)
C. Grebogi, E. Ott, J.A. Yorke, Physica D 7, 181 (1983)
D. Ghosh, B. Roy, Ann. Phys. 353, 222 (2015)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sayeed Anwar, M., Sar, G.K., Ray, A. et al. Behavioral study of a new chaotic system. Eur. Phys. J. Spec. Top. 229, 1343–1350 (2020). https://doi.org/10.1140/epjst/e2020-900250-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2020-900250-6