Nonlinear Dynamical Systems Under Uncertainty, Noise, and Time Delays

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 30 December 2026 | Viewed by 375

Editor


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Guest Editor
Geology Department, Jaroslav Černi Water Institute, Jaroslava Černog 80, 11226 Belgrade, Serbia
Interests: nonlinear dynamics; chaos theory; numerical simulation; geological modeling

Special Issue Information

Dear Colleagues,

This Special Issue invites contributions addressing the behavior of nonlinear dynamical systems under uncertainty, noise, and time delays, with a particular emphasis on natural systems. Such systems—ranging from biological networks and ecological dynamics to geological and hydrogeological processes—are inherently complex, multiscale, and subject to stochastic influences and delayed feedback mechanisms.

We welcome original research and review papers that advance theoretical, numerical, or experimental understanding of how uncertainty and noise shape system stability, transitions, and emergent behavior. Of special interest are studies on phenomena such as pattern formation, tipping points, resilience, synchronization, and failure processes in natural environments, including seismic activity, groundwater flow, climate-driven processes, and biological regulation systems.

Contributions may include novel modeling frameworks, data-driven approaches, or hybrid methods integrating deterministic and stochastic dynamics. Papers that link theory with real-world observations or engineering applications are particularly encouraged.

This Special Issue aims to foster interdisciplinary dialogue and provide new insights into predicting, managing, and mitigating risks in natural systems governed by nonlinear, uncertain, and time-delayed dynamics.

Dr. Srđan Kostić
Guest Editor

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Keywords

  • time delay
  • synchronization
  • nonlinear dynamics
  • chaos
  • complex systems
  • bifurcation
  • bursting

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Published Papers (1 paper)

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Research

35 pages, 4600 KB  
Article
Path-Dependent Landslide Initiation Through Response-Generated Memory Under Mainshock–Aftershock Loading
by Srđan Kostić and Nebojša Vasović
Mathematics 2026, 14(17), 3122; https://doi.org/10.3390/math14173122 - 31 Aug 2026
Viewed by 143
Abstract
Earthquake sequences can affect slope stability before recovery from an earlier event is complete, yet reduced-order models commonly treat successive earthquakes as independent inputs or prescribe cumulative damage through event-based increments. We introduce a bounded, response-generated memory state into a delayed two-block landslide [...] Read more.
Earthquake sequences can affect slope stability before recovery from an earlier event is complete, yet reduced-order models commonly treat successive earthquakes as independent inputs or prescribe cumulative damage through event-based increments. We introduce a bounded, response-generated memory state into a delayed two-block landslide model. The state reduces incremental friction, evolves exclusively through computed dissipative response, and heals continuously between earthquakes. Its critical value is derived independently from the characteristic roots of the delayed mechanical subsystem. Paired aftershock-only and mainshock–aftershock experiments use corrected accelerograms from the 2011 Redcliffs sequence as recorded inputs rather than calibration data. Across 1255 admissible deterministic comparisons, a subcritical mainshock reduced the aftershock activation threshold in every parameter cell; 1235 threshold intervals were strictly separated, while 20 converged to the aftershock-only limit under strong healing. Threshold reduction was almost entirely determined by retained memory (Spearman rank coefficient ρS = 0.9997). Under stochastic forcing, all 33 primary parameter cells showed the same direction of reduction, and 32 paired 95% bootstrap confidence intervals excluded zero. Independent 4096-realisation ensembles yielded reductions of 18.0–26.2% under white-noise and Ornstein–Uhlenbeck forcing. Resetting memory reproduced the aftershock-only response exactly, whereas removing displacement delay eliminated delayed activation. These results identify a causal mechanism by which a non-activating earthquake can transiently lower the activation threshold of a subsequent event, while distinguishing dimensionless model activation from physical landslide failure. Full article
(This article belongs to the Special Issue Nonlinear Dynamical Systems Under Uncertainty, Noise, and Time Delays)
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