Generation of multiscroll chaotic attractors of a finance system with mirror symmetry | Soft Computing Skip to main content
Springer Nature Link
Log in

Generation of multiscroll chaotic attractors of a finance system with mirror symmetry

  • Soft computing in decision making and in modeling in economics
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Based on the mathematical model of a nonlinear finance system, a novel finance chaotic system that generates mirror symmetric multiscroll chaotic attractors is proposed in this paper. The chaotic dynamical behaviors such as symmetry, chaoticity, bifurcation and boundedness are discussed in detail for the finance system with state variables; interest rate, investment demand and price index. The complex composite symmetrical attractors of finance system with different magnitudes are obtained. Moreover, with the help of multilevel-logic pulse signal, the generation of two pairs of different magnitudes symmetrical attractors are explored. The novel grid composite multiscroll chaotic attractors is one of the most interesting result is found in the finance system. By adjusting the parameters of multilevel-logic pulse signals, the finance system is controlled and a novel grid composite multiscroll chaotic attractor is explored in this article.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Data link

No data link is available for this article as no datasets were generated or analyzed during the current study.

References

  • 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

    Google Scholar 

  • Azam A, Aqeel M, Salman A, Faizan A (2017) Chaotic behaviour of modified stretched-twist-fold flow with fractal property. Nonlinear Dyn 90:1–12

    MATH  Google Scholar 

  • Azam A, Aqeel M, Hussain Z (2021) On the dynamics: existence of chaos and symmetry in Krauseand Robert (KR) flow. Soft Comput 25:2521–2530

    MATH  Google Scholar 

  • Cai G, Huang J (2007) A new finance chaotic attractor. Int J Nonlinear Sci 3:213–220

    MathSciNet  MATH  Google Scholar 

  • Celikovsky S, Chen GR (2002) On a generalized Lorenz canonical form of chaotic system via nonlinear observed approach. Int J Bifurc Chaos 8:1789–1812

    MATH  Google Scholar 

  • Cesare LD, Sportelli M (2005) A dynamics IS-LM model with delayed taxation revenues. Chaos Solitons Fractals 25(1):233–244

    MathSciNet  MATH  Google Scholar 

  • Chen GR, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9:1465–1466

    MathSciNet  MATH  Google Scholar 

  • Elwakil A, Ozoguz S (2003) Chaos in a pulse-excited resonator with self-feedback. Electron Lett 39:831–833

    Google Scholar 

  • Elwakil A, Ozoguz S (2006) Multiscroll chaotic oscillators: the nonautonomous approach. IEEE Trans Circuits Sys I 53(9):862–866

    Google Scholar 

  • Elwakil AS, Ozoguz S, Kennedy MP (2002) Creation of a complex butterfly attractor using a novel Lorenz-type system. IEEE Trans Circuits Syst I 49:527–530

    MathSciNet  MATH  Google Scholar 

  • 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):736–744

    MathSciNet  MATH  Google Scholar 

  • 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

    MathSciNet  MATH  Google Scholar 

  • 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

    MathSciNet  MATH  Google Scholar 

  • Gao Q, Ma J (2009) Chaos and Hopf bifurcation of a finance system. Nonlinear Dyn 58(1–2):209–216

    MathSciNet  MATH  Google Scholar 

  • Gilmore R, Letellier C (2007) The symmetry of chaos. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Goodwin RM (1951) The nonlinear accelerator and the persistence of business cycles. Econometrica 19(1):1–17

    MathSciNet  MATH  Google Scholar 

  • Haiyang F, Minqiang L, Fuzan C (2014) Chaotic dynamics in the software market with network Externalities. Soft Comput 18:509–519

    Google Scholar 

  • 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):1–11

    MathSciNet  MATH  Google Scholar 

  • 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):1480–1492

    Google Scholar 

  • Hong Q, Xie Q, Shen Y, Wang X (2016) Generating multi-double-scroll attractors via nonautonomous approach. Chaos 26(8):130–141

    MathSciNet  MATH  Google Scholar 

  • Hong Q, Xie Q, Xiao P (2017) A novel approach for generating multi-direction multi–double-scroll attractors. Nonlinear Dyn 87(2):1015–1030

    Google Scholar 

  • 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):496–500

    Google Scholar 

  • Jiayi F, Wenjing X, Yi H, Dinesh RJ (2021) Application of chaos cuckoo search algorithm in computer vision technology. Soft Comput 25:12373–12387

    Google Scholar 

  • Javeria A, Aqeel M, Salman A, Zainab R (2020) Absolute control of chaotic responses in Robbins disc Dynamo. Eur Phys J plus 135:307

    Google Scholar 

  • Jh L, Chen GR (2002) A new chaotic attractor coined. Int J Bifurc Chaos 3:659–661

    MathSciNet  MATH  Google Scholar 

  • Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141

    MathSciNet  MATH  Google Scholar 

  • 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):2671–2691

    MathSciNet  MATH  Google Scholar 

  • 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):1236–1242

    MathSciNet  Google Scholar 

  • 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 24:4333–4341

    MATH  Google Scholar 

  • Peng X, Zeng Y (2020) A simple method for generating mirror symmetry composite multiscroll chaotic attractors. Int J Bifurc Chaos 30(11):2050220

    MathSciNet  MATH  Google Scholar 

  • Rai V, Upadhyay RK (2004) Chaotic population dynamics and biology of top predator. Chaos Solitons Fractals 21(5):1195–1204

    MathSciNet  MATH  Google Scholar 

  • Rossler OE (1976) An equation for continuous chaos. Phys Lett A 57:397–398

    MATH  Google Scholar 

  • Al Azzawi SF (2004) Stability and bifurcation of pan chaotic system by using Routh-Hurwitz and gardan methods. Appl Math Comput 219(3):1144–1152

    MathSciNet  MATH  Google Scholar 

  • Shahverdiev EM (1999) Boundedness of dynamical systems and chaos synchronization. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip 60(4):3905–3909

    Google Scholar 

  • Sprott JC (1994) Some simple chaotic flows. Phys Rev E 50:647–650

    MathSciNet  Google Scholar 

  • 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 27:1–16

    MathSciNet  MATH  Google Scholar 

  • 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

    MathSciNet  Google Scholar 

  • 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 8:193–205

    Google Scholar 

  • Vlad A, Pasco P, Morariu N (2010) Chaos models in economics. J Comput 12(1):79–83

    Google Scholar 

  • Yalcin ME (2007) Increasing the entropy of a random number generator using n-scroll chaotic attractors. Int J Bifurc Chaos 17(12):4471–4479

    Google Scholar 

  • Yang T (2020) Dynamical analysis of a finance system with nonconstant elasticity of demand. Int J Bifurc Chaos 30(10):2050148

    MathSciNet  MATH  Google Scholar 

  • Yu S, Lü 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):1015–1028

    MathSciNet  MATH  Google Scholar 

  • Zhang C, Yu S (2010) On constructing complex grid multi-wing hyperchaotic system: theoretical design and circuit implementation. Int J Circ Th Appl 41:221–237

    Google Scholar 

  • 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):4575–4580

    Google Scholar 

  • 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 27:1–14

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We are thankful to Higher Education Commission (HEC), Pakistan and Institute of Space Technology (IST), Pakistan for providing a good atmosphere to complete this research work.

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, 44000, Pakistan

    Anam Azam, Danish Ali Sunny & Muhammad Aqeel

Authors
  1. Anam Azam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Danish Ali Sunny
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Aqeel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Danish Ali Sunny.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Azam, A., Sunny, D.A. & Aqeel, M. Generation of multiscroll chaotic attractors of a finance system with mirror symmetry. Soft Comput 27, 2769–2782 (2023). https://doi.org/10.1007/s00500-022-07501-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-022-07501-1

Keywords

Search

Navigation