Chaoslike behavior in nonchaotic systems at finite computation precision

Area of Science:

• Dynamical Systems
• Nonlinear Dynamics
• Computational Physics

Background:

• Investigating the dynamical behavior of two-dimensional maps is crucial for understanding complex systems.
• Identifying conditions that lead to unexpected system behaviors is a key challenge in nonlinear dynamics.

Purpose of the Study:

• To numerically investigate the dynamical behavior of a two-dimensional map.
• To characterize a novel chaos-like behavior observed in nonchaotic system states.

Main Methods:

• Numerical investigation of a two-dimensional map.
• Analysis of Lyapunov exponents to determine system state (chaotic or nonchaotic).

Main Results:

• Chaos-like behavior, including nonsmooth attractor distribution and apparent sensitive dependence on initial conditions, was observed in nonchaotic system states (both Lyapunov exponents nonpositive).
• This behavior is linked to positive local Lyapunov exponent segments within the mode of the second negative Lyapunov exponent.

Conclusions:

• The observed chaos-like behavior in nonchaotic systems is a significant finding with implications for dynamical systems theory.
• This phenomenon may be common in numerical computations and experiments due to inevitable small noise.