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The situated HKB model: how sensorimotor spatial coupling can alter oscillatory brain dynamics.

Aguilera M, Bedia MG, Santos BA, Barandiaran XE - Front Comput Neurosci (2013)

Bottom Line: These results are compared with two different models: a decoupled HKB with no sensory input and a passively-coupled HKB that is also decoupled but receives a structured input generated by a situated agent.We also present the notion of neurodynamic signature as the dynamic pattern that correlates with a specific behavior and we show how only a situated agent can display this signature compared to an agent that simply receives the exact same sensory input.Finally, we discuss the limitations and possible generalization of our model to contemporary neuroscience and philosophy of mind.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science and Engineering Systems, University of Zaragoza Zaragoza, Spain.

ABSTRACT
Despite the increase of both dynamic and embodied/situated approaches in cognitive science, there is still little research on how coordination dynamics under a closed sensorimotor loop might induce qualitatively different patterns of neural oscillations compared to those found in isolated systems. We take as a departure point the Haken-Kelso-Bunz (HKB) model, a generic model for dynamic coordination between two oscillatory components, which has proven useful for a vast range of applications in cognitive science and whose dynamical properties are well understood. In order to explore the properties of this model under closed sensorimotor conditions we present what we call the situated HKB model: a robotic model that performs a gradient climbing task and whose "brain" is modeled by the HKB equation. We solve the differential equations that define the agent-environment coupling for increasing values of the agent's sensitivity (sensor gain), finding different behavioral strategies. These results are compared with two different models: a decoupled HKB with no sensory input and a passively-coupled HKB that is also decoupled but receives a structured input generated by a situated agent. We can precisely quantify and qualitatively describe how the properties of the system, when studied in coupled conditions, radically change in a manner that cannot be deduced from the decoupled HKB models alone. We also present the notion of neurodynamic signature as the dynamic pattern that correlates with a specific behavior and we show how only a situated agent can display this signature compared to an agent that simply receives the exact same sensory input. To our knowledge, this is the first analytical solution of the HKB equation in a sensorimotor loop and qualitative and quantitative analytic comparison of spatially coupled vs. decoupled oscillatory controllers. Finally, we discuss the limitations and possible generalization of our model to contemporary neuroscience and philosophy of mind.

No MeSH data available.


Related in: MedlinePlus

Eigenvalues (λ1, λ2, and λ3) of the attractor (left) and repeller (right) fixed points of the situated-HKB: force of the attraction/repulsion vs. variation of the control parameter s. Real part (solid), Imaginary part (dashed).
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Figure 4: Eigenvalues (λ1, λ2, and λ3) of the attractor (left) and repeller (right) fixed points of the situated-HKB: force of the attraction/repulsion vs. variation of the control parameter s. Real part (solid), Imaginary part (dashed).

Mentions: Computing the Jacobian matrix of the system at the fixed points, and making an eigenvectors/eigenvalues analysis, we get the behavior of our dynamical system around the regions of its state space that bear qualitative significance. In Figure 4, it is illustrated the range of different values of the eigenvalues (denoted by λ1, λ2, and λ3) at each of the fixed points, depending on the parameter s (that corresponds to different observed behavioral patterns for gradient climbing, see Figure 3). We find regions that present simple attractor/repulsion dynamics (when λ1, λ2, λ3 are real numbers) whereas other regions present spiral attractions/repulsions (when λ1, λ2, λ3 have complex values).


The situated HKB model: how sensorimotor spatial coupling can alter oscillatory brain dynamics.

Aguilera M, Bedia MG, Santos BA, Barandiaran XE - Front Comput Neurosci (2013)

Eigenvalues (λ1, λ2, and λ3) of the attractor (left) and repeller (right) fixed points of the situated-HKB: force of the attraction/repulsion vs. variation of the control parameter s. Real part (solid), Imaginary part (dashed).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3750630&req=5

Figure 4: Eigenvalues (λ1, λ2, and λ3) of the attractor (left) and repeller (right) fixed points of the situated-HKB: force of the attraction/repulsion vs. variation of the control parameter s. Real part (solid), Imaginary part (dashed).
Mentions: Computing the Jacobian matrix of the system at the fixed points, and making an eigenvectors/eigenvalues analysis, we get the behavior of our dynamical system around the regions of its state space that bear qualitative significance. In Figure 4, it is illustrated the range of different values of the eigenvalues (denoted by λ1, λ2, and λ3) at each of the fixed points, depending on the parameter s (that corresponds to different observed behavioral patterns for gradient climbing, see Figure 3). We find regions that present simple attractor/repulsion dynamics (when λ1, λ2, λ3 are real numbers) whereas other regions present spiral attractions/repulsions (when λ1, λ2, λ3 have complex values).

Bottom Line: These results are compared with two different models: a decoupled HKB with no sensory input and a passively-coupled HKB that is also decoupled but receives a structured input generated by a situated agent.We also present the notion of neurodynamic signature as the dynamic pattern that correlates with a specific behavior and we show how only a situated agent can display this signature compared to an agent that simply receives the exact same sensory input.Finally, we discuss the limitations and possible generalization of our model to contemporary neuroscience and philosophy of mind.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science and Engineering Systems, University of Zaragoza Zaragoza, Spain.

ABSTRACT
Despite the increase of both dynamic and embodied/situated approaches in cognitive science, there is still little research on how coordination dynamics under a closed sensorimotor loop might induce qualitatively different patterns of neural oscillations compared to those found in isolated systems. We take as a departure point the Haken-Kelso-Bunz (HKB) model, a generic model for dynamic coordination between two oscillatory components, which has proven useful for a vast range of applications in cognitive science and whose dynamical properties are well understood. In order to explore the properties of this model under closed sensorimotor conditions we present what we call the situated HKB model: a robotic model that performs a gradient climbing task and whose "brain" is modeled by the HKB equation. We solve the differential equations that define the agent-environment coupling for increasing values of the agent's sensitivity (sensor gain), finding different behavioral strategies. These results are compared with two different models: a decoupled HKB with no sensory input and a passively-coupled HKB that is also decoupled but receives a structured input generated by a situated agent. We can precisely quantify and qualitatively describe how the properties of the system, when studied in coupled conditions, radically change in a manner that cannot be deduced from the decoupled HKB models alone. We also present the notion of neurodynamic signature as the dynamic pattern that correlates with a specific behavior and we show how only a situated agent can display this signature compared to an agent that simply receives the exact same sensory input. To our knowledge, this is the first analytical solution of the HKB equation in a sensorimotor loop and qualitative and quantitative analytic comparison of spatially coupled vs. decoupled oscillatory controllers. Finally, we discuss the limitations and possible generalization of our model to contemporary neuroscience and philosophy of mind.

No MeSH data available.


Related in: MedlinePlus