Nonlinear Functions Interrelating Neural Activity Recorded Simultaneously from Olfactory Bulb, Somatomotor, Auditory, Visual and Entorhinal Cortices of Awake, Behaving Cats

  • G. Gaál
  • W. J. Freeman


Population coding algorithms have been designed to retrodict sensory stimuli or predict motor behavior from neuronal responses (Georgopoulos et al., 1986). These include calculation of Jacobian matrices in nonlinear systems (Gaál, 1995). which made it possible to model the visuomotor hand movement task of reaching in a plane, in adaptive feedback control while updating the joint angles of a three-joint arm (Lee and Kil, 1994). The control signal was the dot product between the visual error signal and the transpose of the Jacobian matrix of the direct kinematic equation of hand movement. The trajectories of the hand were synchronized with the x and y time series outputs of coupled nonlinear equations. The equations used to calculate the adaptive feedback signal were similar to those used by Kocarev et al. (1993) to show that two different nonlinear systems could synchronize, when the difference between the goal (Lorenz system) and target signals (Chua system) was added as an adaptive feedback signal to modify the equations of the entrained (Chua) system. In robotics, the Jacobian matrix was defined by the makers of the robots. In biological systems, the matrix needs to be derived from observed time series. Experimental control and synchronization of chaos in nonlinear dynamical systems by self-controlling feedback have already been demonstrated (Pyragas, 1992; Pecora and Carroll, 1990; McKenna et al., 1994; Kelso and Ding, 1992), with applications in neurobiological control, prediction and synchronization.


Conditioned Stimulus Olfactory Bulb Jacobian Matrix Entorhinal Cortex Jacobian Matrice 


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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • G. Gaál
    • 1
  • W. J. Freeman
    • 1
  1. 1.Department of Molecular and Cell BiologyUniversity of CaliforniaBerkeleyUSA

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