Reply to "comment on 'how to obtain extreme multistability in coupled dynamical systems' "

Area of Science:

• Physics
• Nonlinear Dynamics
• Control Theory

Background:

• The concept of extreme multistability in dynamical systems has been previously explored by various researchers.
• The significance of conserved quantities in influencing system dynamics is a fundamental aspect applicable across different examples.

Purpose of the Study:

• To address criticisms regarding the novelty of extreme multistability.
• To highlight the role of conserved quantities in dynamical systems.
• To demonstrate the generality of controller design for achieving extreme multistability in coupled systems.

Main Methods:

• Reviewing existing literature on extreme multistability.
• Analyzing the impact of conserved quantities on system dynamics.
• Presenting two novel examples of controller design for coupled systems exhibiting extreme multistability without master-slave behavior.

Main Results:

• The construction of extreme multistability in simple dynamical systems is not a new concept.
• Conserved quantities play a critical role in determining the dynamics of multistable systems.
• Controller designs for coupled systems can achieve extreme multistability without necessarily resulting in master-slave configurations.

Conclusions:

• The findings reaffirm the established understanding of extreme multistability and conserved quantities in dynamical systems.
• The presented examples broaden the scope of controller design for coupled systems, demonstrating flexibility beyond master-slave architectures.