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ABSTRACT Predator‐prey models, such as the Leslie‐Gower model, are essential for understanding population dynamics and stability within ecosystems. These models help explain the balance between species under natural conditions, but the inclusion of factors like the Allee effect and intraspecific competition adds complexity and realism to these interactions, enhancing our ability to predict system behavior under stress. To detect early indicators of population collapse, this study investigates the intricate dynamics of a modified Leslie‐Gower predator‐prey model with both Allee effect and intraspecific competition. We analyze the existence and stability of equilibria, as well as bifurcation phenomena, including saddle‐node bifurcations of codimension 2, Hopf bifurcations of codimension 2, and Bogdanov‐Takens bifurcations of codimension at least 4. Detailed transitions between bifurcation curves–specifically saddle‐node, Hopf, homoclinic, and limit cycle bifurcations–are also examined. We observe a novel transition phenomenon, where a system jumps from saddle‐node bifurcation to homoclinic and limit cycle bifurcations. This suggests that burst oscillations may serve as an early warning of system collapse rather than simply a tipping point. Our findings indicate that moderate levels of intraspecific competition or Allee effect support coexistence of both populations, while excessive levels may destabilize the entire biological system, leading to collapse. These insights offer valuable implications for ecological management and the early detection of risks in population dynamics.
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Noise‐induced versus intrinsic oscillation in ecological systems
Abstract Studies of oscillatory populations have a long history in ecology. A first‐principles understanding of these dynamics can provide insights into causes of population regulation and help with selecting detailed predictive models. A particularly difficult challenge is determining the relative role of deterministic versus stochastic forces in producing oscillations. We employ statistical physics concepts, including measures of spatial synchrony, that incorporate patterns at all scales and are novel to ecology, to show that spatial patterns can, under broad and well‐defined circumstances, elucidate drivers of population dynamics. We find that when neighbours are coupled (e.g. by dispersal), noisy intrinsic oscillations become distinguishable from noise‐induced oscillations at a transition point related to synchronisation that is distinct from the deterministic bifurcation point. We derive this transition point and show that it diverges from the deterministic bifurcation point as stochasticity increases. The concept of universality suggests that the results are robust and widely applicable.
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- Award ID(s):
- 1840221
- PAR ID:
- 10419563
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Ecology Letters
- Volume:
- 25
- Issue:
- 4
- ISSN:
- 1461-023X
- Page Range / eLocation ID:
- p. 814-827
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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