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An actively controlled Susceptible-Infected-Susceptible (actSIS) contagion model is presented for studying epidemic dynamics with continuous-time feedback control of infection rates. Our work is inspired by the observation that epidemics can be controlled through decentralized disease-control strategies such as quarantining, sheltering in place, social distancing, etc., where individuals can actively modify their contact rates in response to observations of the infection levels in the population. Accounting for a time lag in observations and categorizing individuals into distinct sub-populations based on their risk profiles, we show that the actSIS model manifests qualitatively different features as compared with the SIS model. In a homogeneous population of risk-averters, the endemic equilibrium is always reduced, although the transient infection level can overshoot or undershoot. In a homogeneous population of risk-tolerating individuals, the system exhibits bistability, which can also lead to reduced infection. For a heterogeneous population comprised of risk-tolerators and risk-averters, we prove conditions on model parameters for the existence of a Hopf bifurcation and sustained oscillations in the infected population. 

We present a continuous threshold model (CTM) of cascade dynamics for a network of agents with real-valued activity levels that change continuously in time. The model generalizes the linear threshold model (LTM) from the literature, where an agent becomes active (adopts an innovation) if the fraction of its neighbors that are active is above a threshold. With the CTM we study the influence on cascades of heterogeneity in thresholds for a network comprised of a chain of three clusters of agents, each distinguished by a different threshold. The system is most sensitive to change as the dynamics pass through a bifurcation point: if the bifurcation is supercritical the response will be contained, while if the bifurcation is subcritical the response will be a cascade. We show that there is a subcritical bifurcation, thus a cascade, in response to an innovation if there is a large enough disparity between the thresholds of sufficiently large clusters on either end of the chain; otherwise the response will be contained. 

We study distributed cooperative decision-making in a multi-agent stochastic multi-armed bandit (MAB) problem in which agents are connected through an undirected graph and observe the actions and rewards of their neighbors. We develop a novel policy based on partitions of the communication graph and propose a distributed method for selecting an arbitrary number of leaders and partitions. We analyze this new policy and evaluate its performance using Monte-Carlo simulations. 

Constraints on control-dependent processing have become a fundamental concept in general theories of cognition that explain human behavior in terms of rational adaptations to these constraints. However, theories miss a rationale for why such constraints would exist in the first place. Recent work suggests that constraints on the allocation of control facilitate flexible task switching at the expense of the stability needed to support goal-directed behavior in face of distraction. Here, we formulate this problem in a dynamical system, in which control signals are represented as attractors and in which constraints on control allocation limit the depth of these attractors. We derive formal expressions of the stability-flexibility tradeoff, showing that constraints on control allocation improve cognitive flexibility but impair cognitive stability. Finally, we provide evidence that human participants adapt higher constraints on the allocation of control as the demand for flexibility increases but that participants deviate from optimal constraints. 

Abstract Major disturbances can temporarily remove factors that otherwise constrain population abundance and distribution. During such windows of relaxed top‐down and/or bottom‐up control, ungulate populations can grow rapidly, eventually leading to resource depletion and density‐dependent expansion into less‐preferred habitats. Although many studies have explored the demographic outcomes and ecological impacts of these processes, fewer have examined the individual‐level mechanisms by which they occur. We investigated these mechanisms in Gorongosa National Park, where the Mozambican Civil War devastated large‐mammal populations between 1977 and 1992. Gorongosa’s recovery has been marked by proliferation of waterbuck (Kobus ellipsiprymnus), an historically marginal 200‐kg antelope species, which is now roughly 20‐fold more abundant than before the war. We show that after years of unrestricted population growth, waterbuck have depleted food availability in their historically preferred floodplain habitat and have increasingly expanded into historically avoided savanna habitat. This expansion was demographically skewed: mixed‐sex groups of prime‐age individuals remained more common in the floodplain, while bachelors, loners, and subadults populated the savanna. By coupling DNA metabarcoding and forage analysis, we show that waterbuck in these two habitats ate radically different diets, which were more digestible and protein‐rich in the floodplain than in savanna; thus, although individuals in both habitats achieved positive net energy balance, energetic performance was higher in the floodplain. Analysis of daily activity patterns from high‐resolution GPS‐telemetry, accelerometry, and animal‐borne video revealed that savanna waterbuck spent less time eating, perhaps to accommodate their tougher, lower‐quality diets. Waterbuck in savanna also had more ectoparasites than those in the floodplain. Thus, plasticity in foraging behavior and diet selection enabled savanna waterbuck to tolerate the costs of density‐dependent spillover, at least in the short term; however, the already poorer energetic performance of these individuals implies that savanna occupancy may become prohibitively costly as heterospecific competitors and predators continue to recover in Gorongosa. Our results suggest that behavior can provide a leading indicator of the onset of density‐dependent limitation and the likelihood of subsequent population decline, but that reliable inference hinges on understanding the mechanistic basis of observed behavioral shifts.