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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

Comparison of the evolution of the system around the attractor for (A) the situated HKB with s = 2.5 and (B) the decoupled HKB (with Δω = 1, both with a = 5 and b = 1). The black line in the vertical axis represents the evolution over time (right vertical axis) of φ, which has been simulated during 6.5 s with an Euler step of 0.1 with arbitrary initial values of φ = 0.65, η = −2.78, and α = −2.07. The blue line represents the phase space of the HKB, representing the attractors as filled dots and the repellers as empty dots. We observe how the decoupled HKB is only affected by a simple attraction force with constant strength, while a much richer dynamics is shown in the situated HKB, where different forces of attraction interact to modulate the systems evolution.
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Figure 8: Comparison of the evolution of the system around the attractor for (A) the situated HKB with s = 2.5 and (B) the decoupled HKB (with Δω = 1, both with a = 5 and b = 1). The black line in the vertical axis represents the evolution over time (right vertical axis) of φ, which has been simulated during 6.5 s with an Euler step of 0.1 with arbitrary initial values of φ = 0.65, η = −2.78, and α = −2.07. The blue line represents the phase space of the HKB, representing the attractors as filled dots and the repellers as empty dots. We observe how the decoupled HKB is only affected by a simple attraction force with constant strength, while a much richer dynamics is shown in the situated HKB, where different forces of attraction interact to modulate the systems evolution.

Mentions: The decoupled HKB is affected by a constant force of attraction/repulsion (see Figure 8A) while the situated HKB is subject to forces in three different dimensions that continuously modulate each other (Figure 8B). Note that even if we were inducing a constant input (anywhere in the input range displayed by the situated system) the result will be equivalent. The next logical step is to question whether the crucial factor when comparing the HKB and the situated HKB systems is the specific structure of the input. In order to address this question we introduce the passively-coupled HKB model where the HKB equation receives the exact same input as the freely behaving situated HKB, but whose output has no effect.


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)

Comparison of the evolution of the system around the attractor for (A) the situated HKB with s = 2.5 and (B) the decoupled HKB (with Δω = 1, both with a = 5 and b = 1). The black line in the vertical axis represents the evolution over time (right vertical axis) of φ, which has been simulated during 6.5 s with an Euler step of 0.1 with arbitrary initial values of φ = 0.65, η = −2.78, and α = −2.07. The blue line represents the phase space of the HKB, representing the attractors as filled dots and the repellers as empty dots. We observe how the decoupled HKB is only affected by a simple attraction force with constant strength, while a much richer dynamics is shown in the situated HKB, where different forces of attraction interact to modulate the systems evolution.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 8: Comparison of the evolution of the system around the attractor for (A) the situated HKB with s = 2.5 and (B) the decoupled HKB (with Δω = 1, both with a = 5 and b = 1). The black line in the vertical axis represents the evolution over time (right vertical axis) of φ, which has been simulated during 6.5 s with an Euler step of 0.1 with arbitrary initial values of φ = 0.65, η = −2.78, and α = −2.07. The blue line represents the phase space of the HKB, representing the attractors as filled dots and the repellers as empty dots. We observe how the decoupled HKB is only affected by a simple attraction force with constant strength, while a much richer dynamics is shown in the situated HKB, where different forces of attraction interact to modulate the systems evolution.
Mentions: The decoupled HKB is affected by a constant force of attraction/repulsion (see Figure 8A) while the situated HKB is subject to forces in three different dimensions that continuously modulate each other (Figure 8B). Note that even if we were inducing a constant input (anywhere in the input range displayed by the situated system) the result will be equivalent. The next logical step is to question whether the crucial factor when comparing the HKB and the situated HKB systems is the specific structure of the input. In order to address this question we introduce the passively-coupled HKB model where the HKB equation receives the exact same input as the freely behaving situated HKB, but whose output has no effect.

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