Decentralized Competition Produces Nonlinear Dynamics Akin to Klinotaxis

Figure 1

(a) Parametrization of the trajectory of a moving system advancing towards a well-defined target. The velocity vector makes an angle with the horizontal and an angle Ω with the vector which points from the system to the target. is defined as the angle between the vector velocity at time , and the target vector at time . (b) Our nonlinear model of klinotaxis. heterogeneous adaptive agents holding strategies each, decide on a specific action using their respective highest scoring strategy from among the that they possess. These are assigned randomly to each agent at the start of the simulation, from the full strategy space to mimic agent (i.e., component) heterogeneity across the agents. The aggregate of their autonomous actions contributes to the rotation of the moving system either clockwise or anticlockwise by an angle . The winning option is decided from the resultant angle as shown. Subsequently, the winning history is updated, announced, and used by each agent as a new input to decide on its next action. Dashes in the list of strategies are used to indicate groups of strategies that, for clarity, are not explicitly written out.