Additomultiplicative Cascades Govern Multifractal Scaling Reliability Across Cardiac, Financial, and Climate Systems.

Area of Science:

• Complex Systems Science
• Statistical Physics
• Nonlinear Dynamics

Background:

• Multifractal scaling mechanisms in complex systems are poorly understood.
• This limits distinguishing healthy from pathological dynamics and predicting system failures.
• Understanding scale-invariant organization is crucial across diverse physical domains.

Purpose of the Study:

• To introduce threshold sensitivity analysis for classifying cascade types in complex systems.
• To examine how scaling reliability varies across moment orders (q) to probe fluctuations.
• To identify a universal diagnostic signature for complex system dynamics.

Main Methods:

• Developed threshold sensitivity analysis, an extension of Chhabra-Jensen's direct method.
• Analyzed scaling reliability using the coefficient of determination (r2) of partition function regressions across moment orders (q).
• Applied the method to cardiac recordings, financial time series, and climate data.

Main Results:

• Discovered a universal diagnostic signature: symmetric expansion of scaling behavior under relaxed r2 thresholds.
• This signature uniquely identifies additomultiplicative cascades, hybrid processes combining additive and multiplicative dynamics.
• The signature was consistent across cardiac, financial, and climate systems, with domain-specific variations.

Conclusions:

• Additomultiplicative organization is a unifying feature of complex adaptive systems.
• Threshold sensitivity analysis provides a mechanistic diagnostic for dysfunction and resilience.
• Environmental constraints shape complexity but do not determine its fundamental principles.