{
  "abstract": "We formulate a chain of damped harmonic oscillators as a mechanical analogy for a single-lane vehicle platoon and show that it reproduces, and yields analytical insight into, the congestion patterns of car-following traffic. Each follower is treated as a point mass m coupled to its leader by a spring of stiffness k2 (spacing-error feedback) and a dashpot of coefficient c (relative-speed feedback), with an additional optimal-velocity (OV) force k1[V(Δx)−v] acting as a non-conservative driving input. The resulting second-order equation is a damped-oscillator chain with headway-tunable effective stiffness K(h)=k1V′(h)−k2, for which the local damping ratio partitions the parameter plane into an active (negatively damped) regime, an overdamped regime, and an underdamped window that supports ringing oscillations. Long-wavelength string-stability analysis yields a closed-form stable band for the OV slope, whose boundaries trace a tongue in the parameter plane. A weakly nonlinear multiple-scale analysis derives amplitude-dependent frequency shifts, centre drift, and nonlinear envelope decay, and recovers a double-well potential that saturates density-wave growth at a finite amplitude. Ring road simulations validate the predictions on two levels: a systematic numerical sweep shows that the zero-growth contour coincides with the analytic band along the whole tongue, and unbiased cycle-resolved measurements follow the analytic amplitude–frequency curve. Although developed for traffic, the construction is generic for dissipative coupled-oscillator chains with non-monotone driving laws.",
  "abstract_shown": true,
  "affiliations": [
    "School of Transportation and Logistics, Shandong Jiaotong University, Jinan 250023, China",
    "School of Rail Transit, Shandong Jiaotong University, Jinan 250023, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Lidong Zhang",
      "orcid": "0000-0002-5589-8271"
    },
    {
      "affs": [
        0
      ],
      "name": "Lichao Duan"
    },
    {
      "affs": [
        1
      ],
      "name": "Liping Feng"
    },
    {
      "affs": [
        0
      ],
      "name": "Qinglian Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eg9wh14wnhnv0.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193600",
  "fulltext_url": null,
  "id": "eg9wh14wnhnv0",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3600",
  "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",
      "2207|Traffic control and management"
    ]
  ],
  "openalex": "W7220456243",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/eg9wh14wnhnv0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193600",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3600"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Stability and Nonlinear Density Waves in a Mass–Spring–Dashpot Damped-Oscillator Traffic Flow Chain",
  "title_text": "Stability and Nonlinear Density Waves in a Mass–Spring–Dashpot Damped-Oscillator Traffic Flow Chain",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/eg9wh14wnhnv0",
  "venue": "Mathematics",
  "versions": []
}