Turing patterns via pinning control in the simplest memristive cellular nonlinear networks

Area of Science:

• Nonlinear Dynamics
• Electronic Circuits
• Pattern Formation

Background:

• Complex patterns emerge in systems of coupled nonlinear dynamical units.
• Turing patterns are extensively studied across various scientific fields using mathematical models.
• Memristive networks offer a novel platform for investigating nonlinear dynamics.

Purpose of the Study:

• To investigate the emergence of Turing patterns in memristive cellular nonlinear networks.
• To explore the use of spatial pinning control for pattern generation.
• To identify the simplest electronic circuit capable of exhibiting Turing instability.

Main Methods:

• Utilizing coupled units composed of a capacitor and a memristor.
• Applying spatial pinning control to induce pattern formation.
• Deriving analytical conditions for Turing pattern emergence.

Main Results:

• Demonstrated the emergence of Turing patterns in the proposed memristive network architecture.
• Identified specific conditions on controlled node density for global pattern generation.
• Established the proposed circuit as the simplest ideal electronic circuit for Turing instability.

Conclusions:

• The proposed memristive cellular nonlinear network with spatial pinning control facilitates Turing pattern formation.
• The circuit architecture represents a significant simplification for studying Turing instability in electronics.
• This work provides a foundation for designing electronic systems capable of complex pattern generation.