Abstract
This study presents a mathematical model based on Fourier decomposition of a sequence of internal signals generated in a complex system by a sequence of external pulses (time series) for characterizing suddenly emerging phenomena as nonlinear transitions. Newly created temporal patterns extracted from internal signal flow (mathematically represented as oscillations with long period) interact as new entities in a multiplicative manner with subsequent pulses from the external time series (already existing entities) in order to generate nonlinear transitions within the system. Such effects are enhanced when the period of external pulses creating new patterns is similar to the settling time of the complex system (this being the condition for an efficient external action). For complex systems where both classical and quantum phenomena generated by external time series are involved, this mathematical model can correctly explain the transition from classical to quantum behaviour (corresponding to a more ordered structure) avoiding typical contradictions generated by analysis performed on transient time intervals or by wave superposition.
Highlights
IntroductionNonlinear phenomena generated by an external time series represented by a sequence of pulses applied upon a complex system can be noticed not just for physical structures, but for biological and human systems
This study presents a mathematical model based on Fourier decomposition of a sequence of internal signals generated in a complex system by a sequence of external pulses time series for characterizing suddenly emerging phenomena as nonlinear transitions
Nonlinear phenomena generated by an external time series represented by a sequence of pulses applied upon a complex system can be noticed not just for physical structures, but for biological and human systems
Summary
Nonlinear phenomena generated by an external time series represented by a sequence of pulses applied upon a complex system can be noticed not just for physical structures, but for biological and human systems . A set of medium-power shocks applied as transverse force upon a crystalline material fixed at both ends can generate significant deformations possible breaking effect which can not be always explained as a superposition of individual effects of each pulse. Transitions generated by periodical phenomena in biological systems cannot be analyzed using a linear model, since genetic mutations are often involved for this reason genetic algorithms were developed. The human behavior is driven by basic concepts created by repetitive aspects from the environment
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