{
  "abstract": "This paper investigates a dynamic Bertrand duopoly model with boundedly rational firms under asymmetric cost structures. Unlike classical formulations based on symmetric costs, we consider a heterogeneous market where one firm faces a quadratic cost function and the other a linear cost structure. We analyze the existence and local stability of the Bertrand–Nash equilibrium, revealing how adjustment speeds and cost asymmetry influence market stability. The results show that excessive price adjustments and increasing cost differences can destabilize the equilibrium through a period-doubling route to chaos, generating unpredictable price dynamics. The chaotic behavior is characterized using bifurcation analysis, Lyapunov exponents, basin of attraction analysis, and the 0–1 chaos test. Furthermore, a feedback control strategy is developed to suppress chaotic fluctuations and restore the Nash equilibrium. By integrating asymmetric cost structures, global stability analysis, chaos detection, and control mechanisms within a Bertrand framework, this study extends existing symmetric-cost models and provides new insights into stabilizing competitive markets. Numerical simulations confirm the theoretical findings and highlight the role of cost heterogeneity and adjustment mechanisms in shaping the stability and predictability of price competition.",
  "abstract_shown": true,
  "affiliations": [
    "Laboratory of Mathematics and Their Interactions, Department of Mathematics, Abdelhafid Boussouf University, Mila 43000, Algeria",
    "Department of Applied Mathematics, Abdelhafid Boussouf University, R.P. 26, Mila 43000, Algeria",
    "Laboratoire Jean Alexandre Dieudonné, CNRS, Université Côte d’Azur, Campus Sciences, Parc Valrose, 28 Avenue Valrose, 06108 Nice Cedex 02, France",
    "Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 30002, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mourad Azioune",
      "orcid": "0009-0003-7618-4053"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Messaoud Berkal",
      "orcid": "0000-0002-4768-8442"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Mohammed-Salah Abdelouahab",
      "orcid": "0000-0002-9235-8362"
    },
    {
      "affs": [
        2
      ],
      "name": "René Lozi",
      "orcid": "0000-0003-0451-4255"
    },
    {
      "affs": [
        3
      ],
      "name": "Mohammed Bakheet Almatrafi",
      "orcid": "0000-0002-6859-2028"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dk153fnh35bx0.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15100725",
  "fulltext_url": null,
  "id": "dk153fnh35bx0",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/10/725",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3109|Chaos control and synchronization"
    ]
  ],
  "openalex": "W7214971984",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/dk153fnh35bx0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15100725",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/10/725"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Chaos control and synchronization",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Nonlinear Dynamics, Bifurcation, Basin Analysis, and Chaos Control in an Asymmetric-Cost Bertrand Duopoly Model",
  "title_text": "Nonlinear Dynamics, Bifurcation, Basin Analysis, and Chaos Control in an Asymmetric-Cost Bertrand Duopoly Model",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/dk153fnh35bx0",
  "venue": "Axioms",
  "versions": []
}