title: Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model.
abstract: Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics.
authors.affiliation: Institute of Neuroscience, Newcastle University, Framlington Place, Newcastle upon Tyne NE2 4HH, United Kingdom.
authors.forename: Christoforos A
authors.initials: CA
authors.lastname: Papasavvas
authors.affiliation: Interdisciplinary Computing and Complex Biosystems (ICOS) Research Group, School of Computing Science, Newcastle University, Claremont Tower, Newcastle upon Tyne NE1 7RU, United Kingdom.
authors.forename: Yujiang
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Institute of Neuroscience, Newcastle University, Framlington Place, Newcastle upon Tyne NE2 4HH, United Kingdom.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Trevelyan
authors.affiliation: Institute of Neuroscience, Newcastle University, Framlington Place, Newcastle upon Tyne NE2 4HH, United Kingdom.|Interdisciplinary Computing and Complex Biosystems (ICOS) Research Group, School of Computing Science, Newcastle University, Claremont Tower, Newcastle upon Tyne NE1 7RU, United Kingdom.
authors.forename: Marcus
authors.initials: M
authors.lastname: Kaiser
mesh_terms: D003198:Computer Simulation; D008959:Models, Neurological; D009433:Neural Inhibition / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D010507:Periodicity