Heterogeneous Cattaneo–Vernotte equation connection to the noisy voter model
We consider a heterogeneous diffusion equation and its corresponding generalization to the Cattaneo-Vernotte equation. It is derived by a combination of the continuity equation and the constitutive relation in various stochastic interpretations of the heterogeneous diffusion process. The heterogeneity in the system is introduced by considering a position-dependent diffusion coefficient. The exact results for the probability density function and the mean-squared displacement are provided. The limiting case of heterogeneous diffusion is analyzed in detail, and the corresponding time-averaged mean-squared displacement is calculated. From the obtained results, an ergodicity breaking is observed.
Authors
- T. Pietrzak (ORCID: https://orcid.org/0000-0001-6979-5874)
- A. Horzela (ORCID: https://orcid.org/0000-0001-8098-2275)
- K. Górska (ORCID: https://orcid.org/0000-0003-4798-9146)
- Trifce Sandev (ORCID: https://orcid.org/0000-0001-9120-3847)
- D. Jankov Maširević
- T. K. Pogány
Institutions
- Obuda University (HU)
- University of Seoul (KR)
- University of Rijeka (HR)
- Macedonian Academy of Sciences and Arts (MK)
- Korea University (KR)
- Institute of Nuclear Physics, Polish Academy of Sciences (PL)
- Institute of Chemistry (CN)
- University of Osijek (HR)
- Ss. Cyril and Methodius University in Skopje (MK)
Publication Details
- Journal
- Chaos An Interdisciplinary Journal of Nonlinear Science
- Published
- 2026-04-01
- DOI
- https://doi.org/10.1063/5.0325574
- Primary Topic
- Mathematical Biology Tumor Growth
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Narodowe Centrum Nauki
- Narodowa Agencja Wymiany Akademickiej
- Alliance of International Science Organizations