No abstract

The problems we face at all levels in the world today resist unilateral solutions. While the web of interdependencies tightens, our capacity for thinking in terms of dynamic interdependencies has not kept pace. As the gap between the nature of our problems and the ability to understand them grows, we face increasing perils on a multitude of fronts. Systems thinking and one of its subsets-system d ynamics-are important for developing effective strategies to close this gap. Unfortunately, system dynamicists and systems thinkers have not effectively taught their frame-

As monkeys perform schedules containing several trials with a visual cue indicating reward proximity, their error rates decrease as the number of remaining trials decreases, suggesting that their motivation and/or reward expectancy increases as the reward approaches. About one-third of single neurons recorded in the anterior cingulate cortex of monkeys during these reward schedules had responses that progressively changed strength with reward expectancy, an effect that disappeared when the cue was random. Alterations of this progression could be the basis for the changes from normal that are reported in anterior cingulate population activity for obsessive-compulsive disorder and drug abuse, conditions characterized by disturbances in reward expectancy.

in the mammalian nervous system remain active in the absence of stimuli. This activity falls into two main patterns: steady firing at low rates and rhythmic bursting. How are these firing patterns generated? Specifically, how do dynamic interactions between excitatory and inhibitory neurons produce these firing patterns, and how do networks switch from one firing pattern to the other? We investigated these questions theoretically by examining the intrinsic dynamics of large networks of neurons. Using both a semianalytic model based on mean firing rate dynamics and simulations with large neuronal networks, we found that the dynamics, and thus the firing patterns, are controlled largely by one parameter, the fraction of endogenously active cells. When no endogenously active cells are present, networks are either silent or fire at a high rate; as the number of endogenously active cells increases, there is a transition to bursting; and, with a further increase, there is a second transition to steady firing at a low rate. A secondary role is played by network connectivity, which determines whether activity occurs at a constant mean firing rate or oscillates around that mean. These conclusions require only conventional assumptions: excitatory input to a neuron increases its firing rate, inhibitory input decreases it, and neurons exhibit spike-frequency adaptation. These conclusions also lead to two experimentally testable predictions: 1) isolated networks that fire at low rates must contain endogenously active cells and 2) a reduction in the fraction of endogenously active cells in such networks must lead to bursting.