The occurrence of chaos in basic Lotka-Volterra models of four competing species is studied. A brute-force numerical search conditioned on the largest Lyapunov exponent indicates that chaos occurs in a narrow region of parameter space but is robust to perturbations. The dynamics of the attractor are studied using symbolic dynamics, and the question of self-organized critical behavior (scale-invariance) of the solution is considered.

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Nanoparticulate MnO2thin films fabricated by the sol-gel process have been shown to be an outstanding novel electrode material for Ultracapacitors. The average specific capacitance of sol-gel-derived MnO2thin-films on nickel substrates as determined by cyclic voltammetry ranged from 566 to 698 F/g. These films also exhibited good cycling stability within the potential range of 0.0-0.9V (vs SCE) in unbuffered aqueous electrolyte. Both CV and XPS studies showed that MnO2films have remained chemically and structurally intact after 1,500 cycles. The XRD spectra and SEM micrographs showed that the microstructure of MnO2thin films are highly porous, and poorly crystalline or amorphous in nature. The high specific capacitance of MnO2may be predominantly due to pseudocapacitance associated with homogenous and reversible redox reactions of proton insertion into and out of the MnO2lattice. Any variation in the microstructure and thickness of films might affect proton mobility within the oxide matrix and thereby affecting their cycling behaviors. Further optimization of the cycling behaviors is envisaged with better microstructural and thickness control of these sol-gelderived nanoparticulate MnO2thin films.

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