Neimark–Sacker bifurcation analysis and complex nonlinear dynamics in a heterogeneous quadropoly game with an isoelastic demand function

Neimark–Sacker bifurcation analysis and complex nonlinear dynamics in a heterogeneous... In this paper, a nonlinear quadropoly game based on Cournot model with fully heterogeneous players is established. This game extends the model introduced by Tramontana and Elsadany (Nonlinear Dyn 68:187–193, 2012) who considered a heterogeneous triopoly game with an isoelastic demand function. Here, four different types of players and potentially different marginal costs are considered. Moreover, the assumption of an isoelastic demand function increases the nonlinearity of the final four-dimensional map. The stability of the resulting discrete-time dynamical system is analyzed. The existence of Neimark–Sacker bifurcation near the Nash equilibrium point of the game is shown. Also, based on the Kuznetsov’s normal form technique for discrete-time system, the stability of the Neimark–Sacker bifurcation is also discussed which indicates that the bifurcation is supercritical. Moreover, it is shown that the Nash equilibrium point of the game undergoes period-doubling (flip) bifurcation. Furthermore, the double route to chaotic dynamics in this model, via flip bifurcations and via Neimark–Sacker bifurcation of the Nash equilibrium point, is illustrated. Coexistence of multi-chaotic attractors of the model is illustrated. Simulation tools like bifurcation diagrams, stability regions of parameters, Lyapunov exponent spectrum, phase plots and basins of attraction are used to verify the complex dynamics of the game. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Neimark–Sacker bifurcation analysis and complex nonlinear dynamics in a heterogeneous quadropoly game with an isoelastic demand function

Loading next page...
 
/lp/springer_journal/neimark-sacker-bifurcation-analysis-and-complex-nonlinear-dynamics-in-uG5xWPaJgC
Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-017-3602-2
Publisher site
See Article on Publisher Site

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial