Systems of operator-differential equations with hysteresis operators can have unstable equilibrium points with an open basin of attraction. Such equilibria can have homoclinic orbits attached to them, and these orbits are robust. In this paper a population dynamics model with hysteretic response of the prey to variations of the predator is introduced. In this model the prey moves between two patches, and the derivative of the Preisach operator is used to describe the hysteretic flow between the patches. A numerical example of a robust homoclinic loop is presented, and a mechanism creating this homoclinic trajectory is discussed.
This paper presents the entire formulation of longitudinal reinforcement minimisation in a concrete structure of known sections and shape under loading by normal force and bending moment. Constraint conditions are given by the conditions of structure reliability in accordance with the relevant codes for ultimate strength and applicability of the sections specified by a designer. Linearization of the non-linear formulation is described, and possibilities of applying linear programming algorithms are discussed. The functioning of the process described is demonstrated on a plane frame structure design. and Obsahuje seznam literatury