The systems considered in this work are composed of weakly coupled, linear and essentially nonlinear (nonlinearizable) components. In Part I of this work we present numerical evidence of energy pumping in coupled nonlinear mechanical oscillators, i.e., of one-way (irreversible) “channeling” of externally imparted energy from the linear to the nonlinear part of the system, provided that the energy is above a critical level. Clearly, no such phenomenon is possible in the linear system. To obtain a better understanding of the energy pumping phenomenon we first analyze the dynamics of the underlying Hamiltonian system (corresponding to zero damping). First we reduce the equations of motion on an isoenergetic manifold of the dynamical flow, and then compute subharmonic orbits by employing nonsmooth transformation of coordinates which lead to nonlinear boundary value problems. It is conjectured that a 1:1 stable subharmonic orbit of the underlying Hamiltonian system is mainly responsible for the energy pumping phenomenon. This orbit cannot be excited at sufficiently low energies. In Part II of this work the energy pumping phenomenon is further analyzed, and it is shown that it is caused by transient resonance capture on a 1:1 resonance manifold of the system.

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Increasing attention is being devoted to the dynamics of interacting local populations of species, especially the role of changes in incidence that affect regional persistence. The status of species in a regional context may be determined more by metapopulation dynamics than by purely demographic birth and death processes. The contrast between local and regional views of species' persistence is illustrated today by discussion of the status of amphibians. The amphibian fauna may provide an important indicator of the impact of anthropogenic disturbance to wetland ecosystems. We assessed the status of 11 amphibian species in southwestern Ontario, Canada, by estimating species richness, changes in presence and absence, and incidence at 97 ponds from 1992 to 1994. We detected a significant reduction in amphibian species richness in one of three regions. This loss of diversity relative to the historical species complement is a consequence of the land use history. We observed surprisingly high turnover of species at ponds, with increased incidence varying from 0.07 to 0.29 species per pond per year, and decreased incidence ranging from 0.16 to 0.30 species per pond per year. The incidence of common species across years included both declines (leopard frog, Rana pipiens) and increases (American toad, Bufo americanus). For eight relatively rare species, losses exceeded gains between 1992 and 1993, but this pattern was reversed between 1993 and 1994. Understanding environmental factors that determine the status of species will require an expanded, large—scale view of groups of populations (metapopulations) and their spatial dynamics.

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