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We provide the scheme for driving a network modelled by dynamical system from one state (“undesired”) to another one. This can be done by changing in time adjustable parameters and require knowledge of the structure of attractors of a system. The process is explained and illustrated by analyzing the two-element network.We provide the scheme for driving a network modelled by dynamical system from one state (“undesired”) to another one. This can be done by changing in time adjustable parameters and require knowledge of the structure of attractors of a system. The process is explained and illustrated by analyzing the two-element network.

We study non‐monotone iterations of solutions of second order boundary value problems in presence of well‐ordered lower and upper functions in contrast to monotone iterations. Monotone iterations are known to converge to solutions with the specific feature that the respective equation of variations is disconjugate in the interval of consideration. Consequently we need to introduce solutions of other types which may be approximated by non‐monotone iterations.

We consider two types of Fucik like spectra, which have somewhat peculiar features. The first one stretches along the bysectrix of the plane of parameters, the second one may contain separated components. Both spectra are significant for existence of solutions to nonlinear boundary value problems with nonlinearities having asymmetric asymptotics.