Abstract A characterization of a semilinear elliptic partial differential equation (PDE) on bounded domain in R n is given terms an infinite-dimensional dynamical system. The system the space boundary data for PDE. This novel approach to problems that enables use systems tools studying corresponding ill-posed, meaning solutions do not exist forwards or backwards time generic initial data. We of...

The Hodgkin and Huxley equations model action potentials in squid giant axons. Variants of these equations are used in most models for electrical activity of excitable membranes. Computational tools based upon the theory of nonlinear dynamical systems are used here to illustrate how the dynamical behavior of the Hodgkin Huxley model changes as functions of two of the system parameters.

First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.

We consider a delayed Holling type II predator-prey system with birth pulse and impulsive harvesting on predator population at different moments. Firstly, we prove that all solutions of the investigated system are uniformly ultimately bounded. Secondly, the conditions of the globally attractive prey-extinction boundary periodic solution of the investigated system are obtained. Finally, the perm...