title: Dynamic Cross-Entropy.
abstract: Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems.
  
  
  
  We introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures.
  
  
  
  Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain.
  
  
  
  To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy.
  
  
  
  The applied technique may offer new approaches to better understand nonlinear brain activity.
authors.affiliation: Non-Invasive Neurostimulation Therapies Lab, Department of Psychiatry, University of British Columbia, Vancouver, British Columbia, Canada. Electronic address: dorianaur@gmail.com.
authors.forename: Dorian
authors.initials: D
authors.lastname: Aur
authors.affiliation: Non-Invasive Neurostimulation Therapies Lab, Department of Psychiatry, University of British Columbia, Vancouver, British Columbia, Canada.
authors.forename: Fidel
authors.initials: F
authors.lastname: Vila-Rodriguez
mesh_terms: D000465:Algorithms; D000818:Animals; D016477:Artifacts; D001921:Brain / Q000502:physiology / Q000503:physiopathology; D004195:Disease Models, Animal; D004565:Electroconvulsive Therapy; D004569:Electroencephalography / Q000379:methods*; D019277:Entropy; D004827:Epilepsy / Q000503:physiopathology / Q000628:therapy; D006801:Humans; D016015:Logistic Models; D017711:Nonlinear Dynamics; D010507:Periodicity; D011336:Probability; D051381:Rats; D012640:Seizures / Q000503:physiopathology / Q000628:therapy; D012815:Signal Processing, Computer-Assisted; D013997:Time Factors
keywords: Brain synchrony; Chaos; Complexity; Entropy; Nonlinear dynamics; Nonlinear resonance