Dynamical Systems : Proceedings of an IIASA (International Institute for Applied Systems Analysis) Workshop on Mathematics of Dynamic Processes Held at Sopron, Hungary, September 9–13, 1985

The investigation of special topics in systems dynamics -uncertain dynamic processes, viability theory, nonlinear dynamics in models for biomathematics, inverse problems in control systems theory-has become a major issue at the System and Decision Sciences Research Program of the International Insti­ tute for Applied Systems Analysis. The above topics actually reflect two different perspectives in the investigation of dynamic processes. The first, motivated by control theory, is concerned with the properties of dynamic systems that are stable under vari­ ations in the systems' parameters. This allows us to specify classes of dynamic systems for which it is possible to construct and control a whole "tube" of trajectories assigned to a system with uncertain parameters and to resolve some inverse problems of control theory within numerically stable solution schemes. The second perspective is to investigate generic properties of dynamic systems that are due to nonlinearity (as bifurcations theory, chaotic behavior, stability properties, and related problems in the qualitative theory of differential systems). Special stress is given to the applications of non­ linear dynamic systems theory to biomathematics and ecoloey. Front Matter....Pages N2-VI Front Matter....Pages 1-1 Resonant Elimination of a Couple of Invariant Closed Curves in the Neighborhood of a Degenerate Hopf Bifurcation of Diffeomorphisms of R 2 ....Pages 3-9 Iterated Holomorphic Maps On The Punctured Plane....Pages 10-28 Front Matter....Pages 29-29 A Viability Approach to Ljapunov’s Second Method....Pages 31-38 Repellers for Generalized Semidynamical Systems....Pages 39-49 Stability for a Linear Functional Differential Equation with Infinite Delay....Pages 50-54 Front Matter....Pages 55-55 The Ljapunov Vector Function Method in the Analysis of Stability and other Dynamic Properties of Nonlinear Systems....Pages 57-69 Permanence for Replicator Equations....Pages 70-91 Front Matter....Pages 93-93 State Estimation for Dynamical Systems by Means of Ellipsoids....Pages 95-105 Singularity Theory for Nonlinear Optimization Problems....Pages 106-128 Modeling, Approximation, and Complexity of Linear Systems....Pages 129-136 Front Matter....Pages 137-137 Cycling in Simple Genetic Systems: II. The Symmetric Cases....Pages 139-153 Traveling Fronts in Parabolic and Hyperbolic Equations....Pages 154-164 Competitive Exclusion by Zip Bifurcation....Pages 165-178 Chaos and the Theory of Elections....Pages 179-188 Spike-Generating Dynamical Systems and Networks....Pages 189-206 Dynamics of First-Order Partial Differential Equations used to Model Self-Reproducing Cell Populations....Pages 207-214 Back Matter....Pages 215-219