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Threshold dynamics for a stage-structured model with non-local impulsive birth in a heterogeneous environment
Yurong Zhang1, Taishan Yi2, Yanyu Xiao3
1School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China.
Journal of Mathematical Biology
|May 21, 2026
Summary
This study models spatially heterogeneous populations with stage structure and non-local births. We found that spatial heterogeneity influences population dynamics, affecting extinction and dispersal patterns.
Area of Science:
- Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Stage-structured population models are crucial for understanding species with complex life cycles.
- Spatial heterogeneity significantly impacts population dynamics, but its effects in impulsive models are less understood.
Purpose of the Study:
- To investigate the influence of spatial heterogeneity on a stage-structured population model with non-local impulsive birth.
- To analyze the threshold dynamics and long-term behavior of such a model.
Main Methods:
- Development of a non-local impulsive reaction-advection-diffusion model incorporating spatial heterogeneity.
- Conversion of the continuous model to a discrete-time recursive system (discrete map).
- Application of asymptotic spectral radius theory for linearized operators and analysis of the discrete map's qualitative properties.
Main Results:
- Established threshold dynamics for the recursive system, including conditions for non-existence, existence, and global attractivity of non-trivial fixed points.
- Demonstrated the significant impact of spatial heterogeneity on population dynamics.
- Identified key parameters influencing population extinction and dispersal patterns.
Conclusions:
- Spatial heterogeneity plays a critical role in the dynamics of stage-structured populations with non-local impulsive births.
- The developed discrete model and analytical techniques provide a robust framework for studying population persistence and spread.
- Numerical simulations confirm theoretical findings and highlight the importance of dispersal and demographic parameters.
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