In mathematics, a heteroclinic network is an invariant set in the phase space of a dynamical system. It can be thought of loosely as the union of more than one heteroclinic cycle. Heteroclinic networks arise naturally in a number of different types of applications, including fluid dynamics and populations dynamics.

The dynamics of trajectories near to heteroclinic networks is intermittent: trajectories spend a long time performing one type of behaviour (often, close to equilibrium), before switching rapidly to another type of behaviour. This type of intermittent switching behaviour has led to several different groups of researchers using them as a way to model and understand various type of neural dynamics.

References

• Kirk, V; Silber, M (1994-11-01). "A competition between heteroclinic cycles". Nonlinearity. 7 (6). IOP Publishing: 1605–1621. Bibcode:1994Nonli...7.1605K. doi:10.1088/0951-7715/7/6/005. ISSN   0951-7715. S2CID   250772340.
• Rabinovich, M.; Volkovskii, A.; Lecanda, P.; Huerta, R.; Abarbanel, H. D. I.; Laurent, G. (2001-07-20). "Dynamical Encoding by Networks of Competing Neuron Groups: Winnerless Competition" (PDF). Physical Review Letters. 87 (6) 068102. American Physical Society (APS). Bibcode:2001PhRvL..87f8102R. doi:10.1103/physrevlett.87.068102. ISSN   0031-9007. PMID   11497865.
• Rabinovich, Mikhail I.; Afraimovich, Valentin S.; Varona, Pablo (2010). "Heteroclinic binding". Dynamical Systems. 25 (3). Informa UK Limited: 433–442. doi:10.1080/14689367.2010.515396. ISSN   1468-9367. S2CID   11334340.
• Ashwin, Peter; Lavric, Aureliu (2010). "A low-dimensional model of binocular rivalry using winnerless competition". Physica D: Nonlinear Phenomena. 239 (9). Elsevier BV: 529–536. Bibcode:2010PhyD..239..529A. doi:10.1016/j.physd.2009.06.018. hdl: 10871/14537 . ISSN   0167-2789.

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