Causal Dynamic Resonance
Many dynamical systems in nature, such as brains and weather systems, are highly nonlinear and complex. Determining information flow among the components that make up these dynamical systems is challenging. If the components are the result of a common process or become synchronized, causality measures typically fail. We previously introduced Cross-Dynamical Delay Differential Analysis (CD-DDA), a nonlinear method for assessing causal influence, along with a complementary approach for dynamical similarity between time series data, Dynamical Ergodicity Delay Differential Analysis (DE-DDA). Here, we show that ``Causal Dynamic Resonance (CDR)'' further improves the false positive rejection rate by adding white noise to the data, without perturbing the underlying dynamical system. This is followed by a study of CDR in coupled R\"ossler systems, where ground truth interactions are known and in invasive intracranial electroencephalographic (iEEG) data from drug-resistant epilepsy patients undergoing presurgical monitoring.