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<p>Understanding the stability and oscillatory behavior of ecological systems under complex interactions remains a central challenge in nonlinear dynamics. In this paper, we develop a comprehensive mathematical framework for a spatial predator-prey model incorporating double delays, spatial memory diffusion, network topology, and feedback control mechanisms. Through analytical bifurcation analysis and extensive numerical simulations, we investigate how ecological parameters, delays, and network structures influence the emergence of sustained oscillations, chaotic dynamics, and species extinction. Our results reveal that delay effects can destabilize populations, but appropriately designed feedback control strategies effectively enhance ecosystem resilience by shifting bifurcation thresholds. These findings provide new insights into the dynamical regulation of ecological networks facing spatial heterogeneity and delays, offering potential strategies for conservation and ecosystem management.</p>

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Delay-induced dynamics and control in predator-prey networks with spatial memory and network topology

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Qianqian Liang,
  • Qianqian Zheng,
  • Jianwei Shen

摘要

Understanding the stability and oscillatory behavior of ecological systems under complex interactions remains a central challenge in nonlinear dynamics. In this paper, we develop a comprehensive mathematical framework for a spatial predator-prey model incorporating double delays, spatial memory diffusion, network topology, and feedback control mechanisms. Through analytical bifurcation analysis and extensive numerical simulations, we investigate how ecological parameters, delays, and network structures influence the emergence of sustained oscillations, chaotic dynamics, and species extinction. Our results reveal that delay effects can destabilize populations, but appropriately designed feedback control strategies effectively enhance ecosystem resilience by shifting bifurcation thresholds. These findings provide new insights into the dynamical regulation of ecological networks facing spatial heterogeneity and delays, offering potential strategies for conservation and ecosystem management.