Even if COR provides methodologies and tools to support community development, there aren't published works illustrating how we can support with COR tools, an assessment of self-governance in an indigenous community. Here we present exploratory research to provide such support to an indigenous association in the Amazon jungle. To address issues of multi-culturalism, we used a creative choice of methods, which included elements of boundary critique, the Viable System Model, rich pictures and social cartography research. We explore the possibilities that this mixed methods approach to COR would offer to clarify the core dilemmas and paradoxes of self-governance for sustainability that such communities are facing. The analysis is done through VSM mapping the community, at different levels and scales of organisation. It reveals key paradoxes and dilemmas of self-governance, which is helping them to collectively decide on action paths and their needs to (re) develop certain adaptive capabilities. Particularly, it shows that loss of power from traditional (spiritual) authorities, and loss of rituals and other cooperative practices have impacted negatively on the indigenous ways of implementing their life plans and respecting sustainability principles. This research contributes to COR, in presenting an innovative application of the VSM in an indigenous community, supported by expert facilitation, as the basis for reflecting on their selfgovernance challenges and acting upon them. It takes into account a more critical and ethnographic approach to research, capable of better dealing with the variety of a multicultural context.

In this paper we study the approximate controllability of semilinear systems on time scale. In order to do so, we first give a complete characterization for the controllability of linear systems on time scale in terms of surjective linear operators in Hilbert spaces. Then we will prove that, under certain conditions on the nonlinear term, if the corresponding linear system is exactly controllable on false[τ−δ,τfalse]T, for any δ∈false(0,τfalse)T, then semilinear system on time scale is approximately controllable on false[0,τfalse]T.

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In this paper we characterize partially the global dynamic of a predator prey model with non constant mortality rate. Concretely, we give necessary and sufficient conditions in order the system be dissipative and permanent. We study the global stability of the nontrivial equilibrium, when it is unique. We show that it is possible the existence of a unique periodic solution which arises from a supercritical Hopf bifurcation and end up through a subcritical Hopf bifurcation; suggesting that the model exhibits new dynamical features which are not present in the classical model; i.e., in the model with constant mortality rate.