Anticipation via canards in excitable systems.

Area of Science:

• Computational Neuroscience
• Theoretical Neuroscience
• Dynamical Systems

Background:

• Neuronal anticipation of incoming signals is a critical function, yet its underlying physiological mechanisms remain poorly understood.
• Existing models often lack a comprehensive explanation for how receiver neurons predict sender dynamics in unidirectionally coupled systems.

Purpose of the Study:

• To propose a novel theoretical framework explaining neuronal anticipation in excitable systems.
• To elucidate the role of a mathematical object, known as a canard, in mediating predictive capabilities of receiver neurons.
• To provide a numerical method for analyzing transient canard effects.

Main Methods:

• Development of a theoretical viewpoint centered on 'canards' to explain anticipation.
• Numerical simulations to quantify the transient effects of canards.
• Application of the framework to established models: van der Pol, FitzHugh-Nagumo, and a Hodgkin-Huxley reduction.

Main Results:

• Demonstrated that canards act as messengers enabling sender prediction in multi-scale excitable systems.
• Validated the canard-mediated anticipation mechanism across diverse models, including radio-wave circuits and biophysical neuronal models.
• Proposed a concrete experimental paradigm for neuroscientists to test these predictions.

Conclusions:

• Canards offer a unifying theoretical explanation for anticipation in excitable systems.
• The proposed framework provides a foundation for understanding predictive coding in neural networks.
• Future research can extend this approach to broader classes of excitable systems and explore further implications for neural computation.