A multiscale dynamical-systems model of karmic processes: formulation, bifurcation structure, interventions, and a stochastic extension

This work presents a multiscale, dimensionless nonlinear dynamical-systems model of karmic processes, formulated as an abstract framework for studying the accumulation, activation, maturation, and consequences of interacting state variables over time. The core deterministic formulation is an 18-dimensional autonomous dynamical system. The study examines its equilibrium structure, stability properties, invariant boundary dynamics, periodic orbits, and parameter-dependent transitions between dynamical regimes. Numerical analyses include the identification and characterization of a stable period-eight orbit, as well as the investigation of candidate bifurcation structures and fold-related behaviour. The work also explores the effects of controlled interventions through numerical experiments. These experiments examine isolated and combined intervention channels, their directional dependence, and the extent to which mixed interventions may produce non-additive effects. The results are parameter- and regime-dependent and should be interpreted within the dimensionless model rather than as calibrated physical or behavioural effects. A stochastic extension is investigated using Ornstein–Uhlenbeck fluctuations applied to the activation logits of an 11-dimensional quasi-steady reduction (M2-11). The numerical experiments quantify persistent threshold-crossing events under different noise amplitudes and correlation times. This stochastic analysis is restricted to the reduced model and does not establish equivalent stochastic behaviour in the full 18-dimensional system. The accompanying supplementary archive provides model implementations, parameter and initial-condition files, numerical datasets, analysis scripts, figure files, audit reports, and original source packages supporting the research. Scope and limitations: The model is theoretical, dimensionless, and has not been empirically calibrated. It is not presented as an experimentally validated law or as a measurement instrument for human behaviour. The period-sixteen orbit remains an unconfirmed numerical candidate; a complete Feigenbaum period-doubling cascade and asymptotic chaos have not been established. Stochastic threshold crossings are not interpreted as certified transitions between attractors. The purpose of this release is to make the model formulation, numerical analyses, and supporting research materials available for inspection, critical assessment, and further development.