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We extend a recently introduced class of exactly solvable models forrecurrent neural networks with competition between 1D nearest neighbour andinfinite range information processing. We increase the potential for furtherfrustration and competition in these models, as well as their biologicalrelevance, by adding next-nearest neighbour couplings, and we allow formodulation of the attractors so that we can interpolate continuously betweensituations with different numbers of stored patterns. Our models are solved bycombining mean field and random field techniques. They exhibit increasinglycomplex phase diagrams with novel phases, separated by multiple first- andsecond order transitions (dynamical and thermodynamic ones), and, uponmodulating the attractor strengths, non-trivial scenarios of phase diagramdeformation. Our predictions are in excellent agreement with numericalsimulations.Comment: 16 pages, 15 postscript figures, Late

Attractor modulation and proliferation in (1 + ∞)-dimensional neural networks