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Abstract

In the past decades, many mathematical approaches to solve complex nonlinear systems in physics have been successfully applied to neuroscience. One of these tools is the concept of linear response functions. However, phenomena observed in the brain emerge from fundatmentally nonlinear interactions and feedback loops rather than from compositins of linear fliters. Here, we review the successes achieved by applying the linear response formalism to topics, such as rhythm generation and synchrony and by incorporating it into modles that combine linear and nonlinear transformations. We also discuss the challenges encountered in the linear response applications and argue that new theoretical concepts are needed to tackle feedback loops and non-equilibrium dynamics which are experimentally observed in neural networkd but are outside of the validity regime of the linear response formalism.