Constructed complex motions and chaos

Area of Science:

• Engineering
• Nonlinear Dynamics
• Complex Systems

Background:

• Nonlinear systems and interactions present significant challenges in engineering.
• Achieving specific complex motions is crucial for desired dynamical behaviors like chaos and bifurcations.

Purpose of the Study:

• To investigate constructed motions and dynamic topology as novel approaches for nonlinear systems.
• To provide methods for quantitatively determining and controlling complex motions in nonlinear engineering.

Main Methods:

• Utilizing mapping dynamics and constructed networks.
• Applying random/discontinuous dynamic theorems.
• Adopting symbolic dynamic abstracts and topological structures.

Main Results:

• Demonstrated quantitative determination of complex motions.
• Enabled the investigation of constructed complex motions to satisfy expected dynamical behaviors.
• Advanced understanding of nonlinear dynamics and system interactions.

Conclusions:

• Constructed motions and dynamic topology offer promising trends for nonlinear engineering.
• The applied theories facilitate the achievement of specific complex motions and global dynamical behaviors.