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<p>We report a breakthrough discovery of Turing-driven spiral defect chaos (SDC) governed by stationary nucleation sites in time-discrete oscillatory systems—a phenomenon defying classical instability paradigms. Unlike conventional SDC requiring spiral tip migration, this novel state features frozen spiral cores that trigger global chaos through random birth-death processes at fixed spatial coordinates while maintaining absolute immobility. Three universal critical behaviors emerge: (1) Spiral lifetimes follow scale-free power-law distributions with a fixed exponent (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(-3.0\)</EquationSource> </InlineEquation>), independent of control parameters; (2) Spiral tip densities exhibit parameter-invariant scaling laws, collapsing onto a single master curve approximating normal distributions; (3) Self-organized criticality enables multiscale pattern coexistence. Theoretical analyses trace this to a Turing bifurcation, where diffusion destabilizes homogeneous periodic states into “static-source/dynamic-propagation” dissipative structures. This mechanism establishes a new paradigm: localized fluctuations at immobilized tips drive global chaos—resolving the paradox of motionless yet destructive spiral cores. Our findings provide fundamental insights for designing cardiac defibrillators exploiting stationary spiral sources and forecasting ecological invasion fronts dominated by critical fluctuations.</p>

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Turing-driven spiral defect chaos with stationary spiral tips: universal criticality in a time-discrete oscillatory system

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月13日

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  • Qun Wang,
  • Jian Gao

摘要

We report a breakthrough discovery of Turing-driven spiral defect chaos (SDC) governed by stationary nucleation sites in time-discrete oscillatory systems—a phenomenon defying classical instability paradigms. Unlike conventional SDC requiring spiral tip migration, this novel state features frozen spiral cores that trigger global chaos through random birth-death processes at fixed spatial coordinates while maintaining absolute immobility. Three universal critical behaviors emerge: (1) Spiral lifetimes follow scale-free power-law distributions with a fixed exponent ( \(-3.0\) ), independent of control parameters; (2) Spiral tip densities exhibit parameter-invariant scaling laws, collapsing onto a single master curve approximating normal distributions; (3) Self-organized criticality enables multiscale pattern coexistence. Theoretical analyses trace this to a Turing bifurcation, where diffusion destabilizes homogeneous periodic states into “static-source/dynamic-propagation” dissipative structures. This mechanism establishes a new paradigm: localized fluctuations at immobilized tips drive global chaos—resolving the paradox of motionless yet destructive spiral cores. Our findings provide fundamental insights for designing cardiac defibrillators exploiting stationary spiral sources and forecasting ecological invasion fronts dominated by critical fluctuations.