Abstract
The hyperchaos and multistability of electron acoustic waves in a quantum plasma model comprising of nondegenerate cold and degenerate hot electrons and stationary ions are investigated. A six-dimensional dynamical system is constructed from the fluid equations of the model considering traveling wave transformation. The stability analysis of the system is done by finding out the equilibria in the inertia frame. It is interesting to investigate that though the novel system is conservative, it can produce hyperchaos for a set of associated parameters. We have also reported the coexistence of many hyperchaotic attractors as the system is extremely sensitive to the initials. The signature of hyperchaos and coexisting hyperchaos in a conservative quantum plasma system has never been reported before.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
[1] R. Devaney, An Introduction to Chaotic Dynamical Systems, Menlopark, CA, The Benjamin/Cummings Publishing Company, 1986.Search in Google Scholar
[2] G. C. Layek, An Introduction to Dynamical Systems and Chaos, New Delhi, Springer, 2015.10.1007/978-81-322-2556-0Search in Google Scholar
[3] S. He, S. Banerjee, and K. Sun, “Complex dynamics and multiple coexisting attractors in a fractional-order microscopic chemical system,” Eur. Phys. J. Spec. Top., vol. 228, no. 1, pp. 195–207, 2019, https://doi.org/10.1140/epjst/e2019-800166-y.Search in Google Scholar
[4] V. G. Ivancevic and T. T. Ivancevic, Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals, Berlin Heidelberg, Springer-Verlag, 2008.10.1007/978-3-540-79357-1Search in Google Scholar
[5] A. Hastings, C. L. Hom, S. Ellner, P. Turchin, H. Charles, and J. Godfray, “Chaos in ecology: Is mother nature a strange attractor?,” Annu. Rev. Ecol. Sysl., vol. 24, pp. 1–33, 1993, https://doi.org/10.1146/annurev.es.24.110193.000245.Search in Google Scholar
[6] H. Natiq, M. R. K. Ariffin, M. R. M. Said, and S. Banerjee, “Enhancing the sensitivity of a chaos sensor for internet of things,” Internet Things, vol. 7, p. 100083, 2019, https://doi.org/10.1016/j.iot.2019.100083.Search in Google Scholar
[7] S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, CRC Press, 2018.10.1201/9780429492563Search in Google Scholar
[8] Z. Hua and Y. Zhou, “One-dimensional nonlinear model for producing chaos,” IEEE Trans. Circ. Sys. I: Reg. Paper., vol. 65, no. 1, pp. 235–246, 2017.10.1109/TCSI.2017.2717943Search in Google Scholar
[9] M. A. Rahim, H. Natiq, N. A. A. Fataf, and S. Banerjee, “Dynamics of a new hyperchaotic system and multistability,” Euro. Phys. J. Plus, vol. 134, no. 10, p. 499, 2019.10.1140/epjp/i2019-13005-5Search in Google Scholar
[10] H. Natiq, S. Banerjee, S. He, M. R. M. Said, and A. Kilicman, “Designing an M-dimensional nonlinear model for producing hyperchaos,” Soliton. Fractals, vol. 114, pp. 506–515, 2018, https://doi.org/10.1016/j.chaos.2018.08.005.Search in Google Scholar
[11] O. E. Rossler, “An equation for hyperchaos,” Phys. Lett., vol. 71, pp. 155–157, 1979, https://doi.org/10.1016/0375-9601(79)90150-6.Search in Google Scholar
[12] T Matsumoto, L Chua, and K Kobayashi, “Hyper chaos: Laboratory experiment and numerical confirmation,” IEEE Trans. Circ. Sys., vol. 33, p. 1143, 1986, https://doi.org/10.1109/tcs.1986.1085862.Search in Google Scholar
[13] T. Kapitanik and L. O. Chua, “Experimental synchronization of chaos using continuous control,” Int. J. Bifur. Chaos, vol. 04, pp. 477–482, 1994.10.1142/S0218127494000368Search in Google Scholar
[14] G. C. Layek and N. C. Pati, “Bifurcations and hyperchaos in magnetoconvection of non-newtonian fluids,” Int. J. Bifur. Chaos, vol. 28, p. 1830034, 2018, https://doi.org/10.1142/s0218127418300343.Search in Google Scholar
[15] G. Ibrahim and S. S. E. H. Elnashaie, “Hyperchaos in acetylcholinesterase enzyme systems,” Chaos, Solit. Fractals, vol. 08, pp. 1977–2007, 1997, https://doi.org/10.1016/s0960-0779(96)00141-5.Search in Google Scholar
[16] S. Yu, J. Lu, X. Yu, and G. Chen, “Design and implementation of grid multiwing hyperchaotic lorenz system family via switching control and constructing super-heteroclinic loops,” IEEE Trans. Circ. Sys. I: Reg. Pap., vol. 59, no. 5, pp. 1015–1028, 2012, https://doi.org/10.1109/tcsi.2011.2180429.Search in Google Scholar
[17] H. Natiq, M. R. M. Said, M. R. K. Ariffin, S. He, L. Rondoni, and S. Banerjee, “Self-excited and hidden attractors in a novel chaotic system with complicated multistability,” Euro. Phys. J. Plus, vol. 133, no. 12, p. 557, 2018, https://doi.org/10.1140/epjp/i2018-12360-y.Search in Google Scholar
[18] H. Natiq, S. Banerjee, M. R. K. Ariffin, and M. R. M. Said, “Can hyperchaotic maps with high complexity produce multistability?,” Chaos: Interdiscipl. J. Nonlinear Sci., vol. 29, p. 1011103, 2019, https://doi.org/10.1063/1.5079886.Search in Google Scholar PubMed
[19] H. Natiq, S. Banerjee, A. P. Misra, and M. R. M. Said, “Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers,” Chaos, Solit. Fractals, vol. 122, pp. 58–68, 2019, https://doi.org/10.1016/j.chaos.2019.03.009.Search in Google Scholar
[20] W. Gekelman, P. Pribyl, H. Birge-Le et al., “Drift waves and chaos in a LAPTAG plasma physics experiment,” Am. J. Phys., vol. 84, no. 2, 2016, https://doi.org/10.1119/1.4936460.Search in Google Scholar
[21] C. Stan, C. P. Cristescu, and A. Dumitru, “Chaos and hyperchaos in a symmetrical discharge plasma: Experiment and modelling,” Univ. Politehnica Buchar. Sci. Bull.-Series A-Appl. Math. Phys., vol. 70, pp. 25–30, 2008.Search in Google Scholar
[22] T. E. Sheridan and W. L. Theisen, “Transition to chaos in a driven dusty plasma,” Phys. Plasmas, vol. 17, 2010, Art no. 013703, https://doi.org/10.1063/1.3298731.Search in Google Scholar
[23] A. Piel, F. Greiner, T. Klinger, H. Klostermann, and A. Rohde, “Chaos in plasmas: A case study in thermionic discharges, dusty and dirty plasmas,” in Noise, and Chaos in Space and in the Laboratory, Boston, MA, Springer, 1994, pp. 501–521.10.1007/978-1-4615-1829-7_43Search in Google Scholar
[24] G. K. Sabavath, P. K. Shaw, A. N. S. Iyengar, I. Banerjee, and S. K. Mahapatra, “Experimental investigation of quasiperiodic-chaotic-quasiperiodic-chaotic transition in a direct current magnetron sputtering plasma,” Phys. Plasmas, vol. 22, 2015, Art no. 082121, https://doi.org/10.1063/1.4928902.Search in Google Scholar
[25] A. Saha and P. Chatterjee, “Solitonic, periodic, quasiperiodic and chaotic structures of dust ion acoustic waves in nonextensive dusty plasmas,” Euro. Phy. J., vol. 69, p. 203, 2015, https://doi.org/10.1140/epjd/e2015-60115-7.Search in Google Scholar
[26] B. Sahu, B. Pal, S. Poria, and R. Roychoudhury, “Nonlinear dynamics of ion acoustic waves in quantum pair-ion plasmas,” J. Plasma Phys., vol. 81, p. 905810510, 2015, https://doi.org/10.1017/s0022377815000768.Search in Google Scholar
[27] D. Weixing, H. Wei, W. Xiaodong, and C. X. Yu, “Quasiperiodic transition to chaos in a plasma,” Phys. Rev. Lett., vol. 70, no. 2, p. 170, 1993, https://doi.org/10.1103/physrevlett.70.170.Search in Google Scholar PubMed
[28] A. P. Misra, D. Ghosh, and A. Roy Chowdhury, “A novel hyperchaos in the quantum Zakharov system for plasmas,” Phys. Lett., vol. 372, no. 9, pp. 1469–1476, 2008, https://doi.org/10.1016/j.physleta.2007.09.054.Search in Google Scholar
[29] P. A. Markowich, C. A. Ringhofer, and C.s Schmeiser, Semiconductor Equations, Wien, Springer-Verlag, 1990.10.1007/978-3-7091-6961-2Search in Google Scholar
[30] M. Marklund and P. K. Shukla, “Nonlinear collective effects in photon-photon and photon-plasma interactions,” Rev. Mod. Phys., vol. 78, no. 2, p. 591, 2006, https://doi.org/10.1103/revmodphys.78.591.Search in Google Scholar
[31] S. H. Glenzer, O. L. Landen, P. Neumayer, et al., “Observations of plasmons in warm dense matter,” Phys. Rev. Lett., vol. 98, pp. 065002, 2007.10.1103/PhysRevLett.98.065002Search in Google Scholar PubMed
[32] J. E. Cross, R. Brian, and G. Gianluca, “Scaling of magneto-quantum-radiative hydrodynamic equations: From laser-produced plasmas to astrophysics,” Astrophys. J., vol. 795, no. 1, p. 59, 2014, https://doi.org/10.1088/0004-637x/795/1/59.Search in Google Scholar
[33] M. Opher, L. O. Silva, D. E. Dauger, V. K. Decyk, and J. M. Dawson, “Nuclear reaction rates and energy in stellar plasmas: The effect of highly damped modes,” Phys. Plasmas, vol. 8, no. 5, pp. 2454–2460, 2001, https://doi.org/10.1063/1.1362533.Search in Google Scholar
[34] G. Chabrier, D. Saumon, and A. Y. Potekhin, “Dense plasmas in astrophysics: from giant planets to neutron stars,” J. Phys. Math. Gen., vol. 39, no. 17, p. 4411, 2006, https://doi.org/10.1088/0305-4470/39/17/s16.Search in Google Scholar
[35] A. K. Harding and Lai Dong, Reports on Progress in Physics, vol. 69, UK, IOP Publishing Ltd, 2006, pp. 2631–2708.10.1088/0034-4885/69/9/R03Search in Google Scholar
[36] S. Chandra, S. N. Paul, and B. Ghosh, “Electron-acoustic solitary waves in a relativistically degenerate quantum plasma with two-temperature electrons,” Astrophys. Space Sci., vol. 343, pp. 213–219, 2013, https://doi.org/10.1007/s10509-012-1097-3.Search in Google Scholar
[37] B. Sahu, B. Pal, S. Poria, and R. Roychoudhury, “Nonlinear dynamics of ion acoustic waves in quantum pair-ion plasmas,” J. Plasma Phys., vol. 81, no. 5, p. 905810510, 2015, https://doi.org/10.1017/s0022377815000768.Search in Google Scholar
[38] U. N. Ghosh, P. Chatterjee, and R. Roychoudhury, “Study of possible chaotic, quasi-periodic and periodic structures in quantum dusty plasma,” Phys. Plasmas, vol. 21, pp. 11113705, 2014, https://doi.org/10.1063/1.4901917.Search in Google Scholar
[39] L. Mandi, A. Saha, and P. Chatterjee, “Dynamics of ion-acoustic waves in Thomas-Fermi plasmas with source ter,” Adv. Space Res., vol. 64, no. 2, pp. 427–435, 2019, https://doi.org/10.1016/j.asr.2019.04.028.Search in Google Scholar
[40] J. S. Richman and J. Randall Moorman, “Physiological time-series analysis using approximate entropy and sample entropy,” Am. J. Physiol. Heart Circ. Physiol., vol. 278, no. 6, pp. H2039–H2049, 2000, https://doi.org/10.1152/ajpheart.2000.278.6.h2039.Search in Google Scholar
[41] F. Kaffashi, R. Foglyano, C. G. Wilson, and K. A. Loparo, “The effect of time delay on approximate & sample entropy calculations,” Phys. Nonlinear Phenom., vol. 237, pp. 3069–3074, 2008, https://doi.org/10.1016/j.physd.2008.06.005.Search in Google Scholar
[42] A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining lyapunov exponents from a time series,” Phys. Nonlinear Phenom., vol. 16, no. 3, pp. 285–317, 1985, https://doi.org/10.1016/0167-2789(85)90011-9.Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Dynamical Systems & Nonlinear Phenomena
- In search of hyperchaos in a high dimensional unmagnetized quantum plasma
- Multistability and chaotic scenario in a quantum pair-ion plasma
- Dust-acoustic Gardner solitons in cryogenic plasma with the effect of polarization in the presence of a quantizing magnetic field
- Quantum Theory
- Trace dynamics and division algebras: towards quantum gravity and unification
- Solid State Physics & Materials Science
- Birefringence and order parameter studies in ferroelectric liquid crystals using laser transmission technique
- Investigations on the g factors and local structure for the trigonal Ce3+ center in YAl3(BO3)4 crystal
- Fiber-optic Fabry–Perot temperature sensor based on the ultraviolet curable glue-filled cavity and two-beam interference principle
- Tuning the properties of RF sputtered tin sulphide thin films and enhanced performance in RF sputtered SnS thin films hetero-junction solar cell devices
Articles in the same Issue
- Frontmatter
- Dynamical Systems & Nonlinear Phenomena
- In search of hyperchaos in a high dimensional unmagnetized quantum plasma
- Multistability and chaotic scenario in a quantum pair-ion plasma
- Dust-acoustic Gardner solitons in cryogenic plasma with the effect of polarization in the presence of a quantizing magnetic field
- Quantum Theory
- Trace dynamics and division algebras: towards quantum gravity and unification
- Solid State Physics & Materials Science
- Birefringence and order parameter studies in ferroelectric liquid crystals using laser transmission technique
- Investigations on the g factors and local structure for the trigonal Ce3+ center in YAl3(BO3)4 crystal
- Fiber-optic Fabry–Perot temperature sensor based on the ultraviolet curable glue-filled cavity and two-beam interference principle
- Tuning the properties of RF sputtered tin sulphide thin films and enhanced performance in RF sputtered SnS thin films hetero-junction solar cell devices