Landscapes of Non-gradient Dynamics Without Detailed Balance: Stable Limit Cycles and Multiple Attractors

Landscape is one of the key notions in literature on biological processes and physics of complex systems with both deterministic and stochastic dynamics. The large deviation theory (LDT) provides a possible mathematical basis for the scientists' intuition. In terms of Freidlin-Wentzell's LDT, we discuss explicitly two issues in singularly perturbed stationary diffusion processes arisen from nonlinear differential equations: (1) For a process whose corresponding ordinary differential equation has a stable limit cycle, the stationary solution exhibits a clear separation of time scales: an exponential terms and an algebraic prefactor. The large deviation rate function attains its minimum zero on the entire stable limit cycle, while the leading term of the prefactor is inversely proportional to the velocity of the non-uniform periodic oscillation on the cycle. (2) For dynamics with multiple stable fixed points and saddles, there is in general a breakdown of detailed balance among the corresponding attractors. Two landscapes, a local and a global, arise in LDT, and a Markov jumping process with cycle flux emerges in the low-noise limit. A local landscape is pertinent to the transition rates between neighboring stable fixed points; and the global landscape defines a nonequilibrium steady state. There would be nondifferentiable points in the latter for a stationary dynamics with cycle flux. LDT serving as the mathematical foundation for emergent landscapes deserves further investigations.Comment: 4 figur

Bridging Contested Terrain: Linking Incentive-Based and Learning Perspectives on Organizational Evolution

In this paper we present a general model of organizational problem-solving in which we explore the relationship between problem complexity, decentralization of tasks and reward schemes. When facing complex problems which require the coordination of large numbers of interdependent elements, organization face a decomposition problem which has both a cognitive dimension and a reward and incentive dimension. The former relates to the decomposition and allocation of the process of generation of new solutions: since the search space is too vast to be searched extensively, organizations employ heuristics for reducing it. The decomposition heuristic takes the form of division of cognitive labor and determines which solutions are generated and become candidates for selection. The reward and incentive dimension defines the selection environment which chooses over alternative solutions. The model we present studies the interrelationships between these two dimensions, in particular we compare the problem solving performance of organizations characterized by various decompositions (of coarser of finer grain) and various reward schemes (at the level of the entire organization, team and individual). Moreover we extend our model in a still tentative fashion - in order to account for such power and authority relationships (giving some parts of the organization the power to stop changes in other parts), and to discuss the co-evolution of problem representations and incentive mechanisms.-

Monk business: an example of the dynamics of organizations.

In this paper we present a dynamic model of an organization. It is shown that the quality of the members of the organization may cycle and that even if the organization promotes excellency, the organization may end up populated by mediocre agents only.Overlapping generations; Quanty organization;

On the Convergence of Evolutionary and Behavioral Theories of Organizations: A Tentative Roadmap

The behavioral theory of the firm has been acknowledged as one of the most fundamental pillars on which evolutionary theorizing in economics has been built. Nelson and Winter’s 1982 book is pervaded by the philosophy and concepts previously developed by Cyert, March and Simon. On the other hand, some behavioral notions, such as bounded rationality, though isolated from the context, are also at the heart of some economic theories of institutions such as transaction costs economics. In this paper, after briefly reviewing the basic concepts of evolutionary economics, we discuss its implications for the theory of organizations (and business firms in particular), and we suggest that evolutionary theory should coherently embrace an “embeddedness” view of organizations, whereby the latter are not simply efficient solutions to informational problems arising from contract incompleteness and uncertainty, but also shape the “visions of the world”, interaction networks, behavioral patterns and, ultimately, the very identity of the agents. After outlining the basic features of this perspective we analyze its consequences and empirical relevance.