TY  - JOUR
AU  - Lin, Dasen
AU  - Muhammadhaji, Ahmadjan
PY  - 2026
DA  - 2026/06/28
TI  - Bifurcation and Stability Analysis in a Spatially Fractional-Order Diffusive Mussel-Algae Model
JO  - Journal of Nonlinear Dynamics and Applications
T2  - Journal of Nonlinear Dynamics and Applications
JF  - Journal of Nonlinear Dynamics and Applications
VL  - 2
IS  - 2
SP  - 127
EP  - 142
DO  - 10.62762/JNDA.2026.807630
UR  - https://www.icck.org/article/abs/JNDA.2026.807630
KW  - Turing-Hopf bifurcation
KW  - fractional-order model
KW  - anomalous superdiffusion
KW  - amplitude equation
AB  - This study elucidates the ramifications of integrating a spatial fractional-order derivative into a diffusive mussel-algae model. While the formation in such models of patterns such as Turing instability, Hopf bifurcation, and Turing-Hopf bifurcation has been extensively scrutinized in prior investigations, the impact of spatial fractional-order derivatives remains largely unknown. Beyond its ecological significance, the fractional diffusion operator is of interest because it elicits novel and nontrivial pattern formations, particularly those emerging from Turing-Hopf bifurcations. Our core objective is to dissect how spatial fractional-order derivatives modulate the spatiotemporal dynamics of a system's solutions. To characterize this degenerate bifurcation within an anomalous diffusion framework, we employ weakly nonlinear analysis to derive the corresponding amplitude equations at the Turing-Hopf bifurcation threshold. Furthermore, a systematic analysis of these amplitude equations under appropriate parametric conditions reveals a rich repertoire of spatiotemporal dynamical behaviors.
SN  - 3069-6313
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Lin2026Bifurcatio,
  author = {Dasen Lin and Ahmadjan Muhammadhaji},
  title = {Bifurcation and Stability Analysis in a Spatially Fractional-Order Diffusive Mussel-Algae Model},
  journal = {Journal of Nonlinear Dynamics and Applications},
  year = {2026},
  volume = {2},
  number = {2},
  pages = {127-142},
  doi = {10.62762/JNDA.2026.807630},
  url = {https://www.icck.org/article/abs/JNDA.2026.807630},
  abstract = {This study elucidates the ramifications of integrating a spatial fractional-order derivative into a diffusive mussel-algae model. While the formation in such models of patterns such as Turing instability, Hopf bifurcation, and Turing-Hopf bifurcation has been extensively scrutinized in prior investigations, the impact of spatial fractional-order derivatives remains largely unknown. Beyond its ecological significance, the fractional diffusion operator is of interest because it elicits novel and nontrivial pattern formations, particularly those emerging from Turing-Hopf bifurcations. Our core objective is to dissect how spatial fractional-order derivatives modulate the spatiotemporal dynamics of a system's solutions. To characterize this degenerate bifurcation within an anomalous diffusion framework, we employ weakly nonlinear analysis to derive the corresponding amplitude equations at the Turing-Hopf bifurcation threshold. Furthermore, a systematic analysis of these amplitude equations under appropriate parametric conditions reveals a rich repertoire of spatiotemporal dynamical behaviors.},
  keywords = {Turing-Hopf bifurcation, fractional-order model, anomalous superdiffusion, amplitude equation},
  issn = {3069-6313},
  publisher = {Institute of Central Computation and Knowledge}
}