Ordered waves in a memristive excitable media under asymmetrical diffusion.

Area of Science:

• Complex systems
• Nonlinear dynamics
• Biophysics

Background:

• Excitable media exhibit complex dynamics influenced by external stimuli.
• Electric fields can induce polarization and shape deformation in flexible media like cardiac tissue.
• Intracellular ion diffusion is crucial for the behavior of excitable systems.

Purpose of the Study:

• To investigate the collective dynamics of excitable media under external electric fields.
• To incorporate memristive electromagnetic induction and shape deformation into excitable medium models.
• To establish an equivalent network framework for analyzing these complex interactions.

Main Methods:

• Development of an extended excitable medium model.
• Incorporation of memristive electromagnetic induction and shape deformation.
• Establishment of an equivalent coupled neural network framework.
• Analysis of reaction-diffusion equations and collective behaviors.

Main Results:

• Shape deformation leads to complementary diffusion coefficients (Dx, Dy) in constant-size media.
• Asymmetrical diffusion, induced by shape changes, modifies wave stability.
• The model successfully explores wave propagation and synchronization stability.
• Memristive current and shape deformation provide a more realistic physical representation.

Conclusions:

• The interplay of memristive induction and shape deformation significantly impacts excitable media dynamics.
• Asymmetrical diffusion is a key factor in modulating wave stability.
• The developed network framework offers insights into collective behaviors in complex systems.
• This integrated approach enhances the physical realism of excitable medium modeling.