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Phantom instabilities in adiabatically driven systems: dynamical sensitivity to computational precision.

Haider Hasan Jafri¹, Thounaojam Umeshkanta Singh, Ramakrishna Ramaswamy

¹School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India.

Chaos (Woodbury, N.Y.)

|October 2, 2012

Summary

This summary is machine-generated.

Numerical precision is crucial for studying nonlinear mappings. Low precision can lead to phantom instabilities, causing deviations from true dynamics in adiabatic systems.

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Area of Science:

Nonlinear dynamics
Dynamical systems theory
Computational physics

Background:

Adiabatically driven nonlinear mappings with skew-product structure exhibit complex dynamical phenomena.
Numerical simulations are essential for analyzing these systems but can be susceptible to precision errors.

Purpose of the Study:

To investigate the robustness of dynamical phenomena in adiabatically driven nonlinear mappings under varying numerical precision.
To understand how inadequate numerical precision affects the observed dynamics, particularly the emergence of instabilities.

Main Methods:

Analysis of nonlinear mappings with skew-product structure under adiabatic driving.
Simulations employing different levels of numerical precision to track orbital behavior.
Examination of deviations from true orbits caused by computational errors.

Main Results:

Inadequate numerical precision leads to deviations from true orbits for monotone, periodic, or quasiperiodic driving.
Slow modulation can 'freeze' orbits, but low precision introduces phantom instabilities.
Observed dynamics are sensitive to numerical precision, with errors building up over time.

Conclusions:

Finite precision computations can misrepresent the true dynamics of adiabatic nonlinear systems.
The minimum required numerical accuracy is linked to the system's internal timescale.
Careful consideration of numerical precision is essential for reliable analysis of these dynamical systems.