Nonlinear Dynamics and Chaos Where do we go from here?

Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such systems? Written by international experts, Nonlinear Dynamics and Chaos: Where Do We Go from Here? assesses what the future holds for dynamics and chaos. The chapters address one or more of the broad and interconnected main themes: neural and biological systems, spatially extended systems, and experimentation in the physical sciences. The contributors offer suggestions as to what they see as the way forward, often in the form of open questions for future research.

PrefaceBifurcation and Degenerate Decomposition in Multiple Time Scale Dynamical Systems John GuckenheimerMany-Body Quantum MechanicsRobert MacKay Unfolding Complexity: Hereditory Dynamical Systems-New Bifurcation Schemes and High Dimensional ChaosUwe an der HeidenCreating Stability out of InstabilityChris JonesSignal or Noise? A Nonlinear Dynamics Approach to Spatiotemporal CommunicationRajarshi RoyOutstanding Problems in the Theory of Pattern FormationEdgar KnoblochIs Chaos Relevant to Fluid Mechanics?Tom MullinTime-Reversed Acoustics and ChaosMathias FinkReduction Methods Applied to Nonlocally Coupled Oscillator SystemsYoshiki KuramotoA Prime Number of Prime Questions about Vortex Dynamics in Nonlinear MediaArt WinfreeSpontaneous Pattern Formation in Primary Visual CortexPaul Bressloff and Jack CowanModels for Pattern Formation in DevelopmentBard ErmentroutSpatiotemporal Nonlinear Dynamics: A New BeginningWilliam DittoAuthor Index