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<p>This work examines a predator prey system subject to tipping effects, where small environmental disturbances may trigger abrupt and irreversible shifts in population dynamics. The model incorporates multiple forms of external stress constant, periodic, and exponentially increasing to capture diverse ecological conditions. To ensure biological relevance, we first establish the positivity of system solutions, followed by a Lyapunov stability analysis of equilibrium states. Bifurcation analysis is then carried out to identify threshold parameters, such as delay and stress intensity, that induce qualitative changes in dynamics. Sensitivity analysis using PRCC shows prey growth rate (<i>r</i>) and carrying capacity (<i>k</i>) strongly promote stability, while high predation rate (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11790_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>) and stress (<i>p</i>) destabilize the system. These results highlight that managing prey productivity and controlling predation pressure are critical for preventing ecological tipping points. The inclusion of predation delay further modifies oscillatory behavior and contributes to complex dynamical outcomes. Our numerical simulations support the analytical findings, showing how different stressor profiles, combined with tipping effects and delays, can generate stability switches, sustained oscillations, and chaotic patterns. Overall, the study advances understanding of ecological resilience and underscores the vulnerability of predator prey systems to environmental perturbations.</p>

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Uncovering ecological thresholds: stress-driven response, time delay, and intraspecies competition among predators in predator–prey dynamics

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • David Raju Thommandru,
  • Soumen Kundu

摘要

This work examines a predator prey system subject to tipping effects, where small environmental disturbances may trigger abrupt and irreversible shifts in population dynamics. The model incorporates multiple forms of external stress constant, periodic, and exponentially increasing to capture diverse ecological conditions. To ensure biological relevance, we first establish the positivity of system solutions, followed by a Lyapunov stability analysis of equilibrium states. Bifurcation analysis is then carried out to identify threshold parameters, such as delay and stress intensity, that induce qualitative changes in dynamics. Sensitivity analysis using PRCC shows prey growth rate (r) and carrying capacity (k) strongly promote stability, while high predation rate ( \(\alpha \) α ) and stress (p) destabilize the system. These results highlight that managing prey productivity and controlling predation pressure are critical for preventing ecological tipping points. The inclusion of predation delay further modifies oscillatory behavior and contributes to complex dynamical outcomes. Our numerical simulations support the analytical findings, showing how different stressor profiles, combined with tipping effects and delays, can generate stability switches, sustained oscillations, and chaotic patterns. Overall, the study advances understanding of ecological resilience and underscores the vulnerability of predator prey systems to environmental perturbations.