Diffusive instability, patterns and limit cycles in a slow-fast generalized SamardzijaGreller model: a multiscale approach
- Title
- Diffusive instability, patterns and limit cycles in a slow-fast generalized SamardzijaGreller model: a multiscale approach
- Creator
- Chakraborty, Arkaprovo; Mukherjee, Nayana; Veeresha, P.
- Description
- The SamardzijaGreller model is an extension of the classical LotkaVolterra predatorprey system, and this paper investigates the multiscale dynamics in a modified SamardzijaGreller model to take into account the slower timescales in predator reactions rather than prey. We present a comprehensive local stability analysis, pattern formation through diffusive instability and fractional Hopf bifurcations. The analysis of the spatio-temporal model reveals the effects of diffusion coefficients and parameter variations on the dynamical behavior of the slow-fast system. By analyzing the systems response to changes in the self-diffusion rate of the prey (dX), the intra-species competition rate of the first predator (d1) and the interaction parameter a, we observe chaotic patterns for small values of a, particularly when the prey exhibits strong diffusion. Increases in a lead to the emergence of regular, periodic patterns that are homogeneous in space. We discuss in detail how fractional-order models create memory effects that inhibit chaotic transitions, potentially being delayed or avoided in the temporal model. The study shows clear differences in the dynamical regimes between the integer-order and the fractional-order models. The latter model gives more significance to the stabilization effect of the fractional-order derivative on ecological systems and improves our understanding of predatorprey interactions under different parameter settings. Findings clarify the potential to derive ecological stability from emergent patterns and transition into a better understanding of complex ecological processes. The Author(s), under exclusive licence to Springer Nature B.V. 2025.
- Source
- Nonlinear Dynamics;Volume;113;Issue;14;Article No.;33127;pp.18037-18058
- Date
- 01-01-2025
- Publisher
- Springer Science and Business Media B.V.
- Subject
- Caputo fractional derivative; Chaos; Fractional Hopf bifurcation; Pattern formation; SamardzijaGreller model
- Coverage
- Chakraborty A., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India; Mukherjee N., Department of Mathematics, Mahindra University, Hyderabad, 500043, India; Veeresha P., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India
- Rights
- Restricted Access; Hardcopy may be available in the library
- Relation
- ISSN: 0924090X; CODEN: NODYE
- Format
- online
- Language
- English
- Type
- Article
Collection
Citation
Chakraborty, Arkaprovo; Mukherjee, Nayana; Veeresha, P., “Diffusive instability, patterns and limit cycles in a slow-fast generalized SamardzijaGreller model: a multiscale approach,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 18, 2026, https://archives.christuniversity.in/items/show/21945.