Error Structure Arising from the Synchronization of Hybrid Chaotic Systems with Mixed Time Delays

• Activity Number: 83
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Morris Morgan* and Carolyn Bradshaw Morgan and Kristin Denise Morgan
• Companies: Hampton University and Hampton University and University of Kentucky
• Keywords: Controller ; ARIMA ; Synchronization ; Time Delay ; Robust ; Chaotic

Abstract

Over the past years the authors have developed a robust statistical error-based controller for synchronizing chaotic systems with and without inherent time delays. For an arbitrary time delay neither local nor global stability is a certainty. Care must be taken to identify such stability pockets prior to implementing the statistical error-based controller design (SEBCD) strategy. Such hybrid systems arise in many physical and biological settings and impose additional constraints on controller design. Our new approach involves generating initial (zero-state) error distributions based on differences between the response and drive signals that are used to estimate stability limits and controller gains only within these stable pockets. In the present investigation, ARIMA models of these synchronization errors are used to develop graphical stability maps that highlight the connections among controller gains and the spectral nature of the resulting ARIMA coefficients.