In this paper, we present a generic theoretical chemotactic model that accounts for certain emergent behaviors observed in ant foraging. The model does not have many of the constraints and limitations of existing models for ants colony dynamics and takes into account the distinctly different behaviors exhibited in nature by ant foragers in search of food and food ferrying ants. Numerical simulations based on the model show trail formation in foraging ant colonies to be an emergent phenomenon and, in particular, replicate behavior observed in experiments involving the species P. megacephala. The results have broader implications for the study of randomness in chemotactic models. Potential applications include the developments of novel algorithms for stochastic search in engineered complex systems such as robotic swarms.
Bibliographical noteFunding Information:
S. Ramakrishnan and M. Kumar acknowledge support from NSF Grant EFRI: 1024608. T. Laurent acknowledges support from NSF Grant DMS: 1414396. A. L. Bertozzi acknowledges support from NSF Grants EFRI: 1024765, DMS: 0907931 and CMMI: 1435709. This work was presented at: (i) NSF BECS Principal Investigator Workshop, National Science Foundation, Arlington VA, March 2011, (ii) 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando FL, July 2012 and (iii) NSF BECS Principal Investigator Workshop, National Science Foundation, Arlington VA, January 2013.
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- Ant foraging
- Complex systems
- Keller-Segel model