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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

Phase space of the extended HKB equation for fixed values of the coupling coefficients a and b. The system exhibits three different kinds of phase space depending on the control parameter Δω, showing multistable (black), monostable (dark gray) or metastable (light gray) dynamics. The filled and empty dots represent respectively the attractors and repellers of the system for different values of Δω. In this paper, the parameters used are choosen to ensure that the monostable region is the only one that is stable for the agent.
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Figure 1: Phase space of the extended HKB equation for fixed values of the coupling coefficients a and b. The system exhibits three different kinds of phase space depending on the control parameter Δω, showing multistable (black), monostable (dark gray) or metastable (light gray) dynamics. The filled and empty dots represent respectively the attractors and repellers of the system for different values of Δω. In this paper, the parameters used are choosen to ensure that the monostable region is the only one that is stable for the agent.

Mentions: The relative phase or phase difference, φ, represents the order parameter or collective variable that emerges from lower-level interactions of the two coupled oscillators, a and b are the coupling coefficients between the two oscillators, and Δω is the difference between their intrinsic frequencies. Despite its simplicity, this equation captures a wide range of self-organized phenomena. Different combinations of the control parameters a, b (or rather b/a) and Δω give rise to different collective behaviors. For example, when shifting the value of Δω while the values of a and b are held fixed, the system experiences phase transitions between three different modes of behavior: monostable, bistable and metastable (Figure 1).


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)

Phase space of the extended HKB equation for fixed values of the coupling coefficients a and b. The system exhibits three different kinds of phase space depending on the control parameter Δω, showing multistable (black), monostable (dark gray) or metastable (light gray) dynamics. The filled and empty dots represent respectively the attractors and repellers of the system for different values of Δω. In this paper, the parameters used are choosen to ensure that the monostable region is the only one that is stable for the agent.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Phase space of the extended HKB equation for fixed values of the coupling coefficients a and b. The system exhibits three different kinds of phase space depending on the control parameter Δω, showing multistable (black), monostable (dark gray) or metastable (light gray) dynamics. The filled and empty dots represent respectively the attractors and repellers of the system for different values of Δω. In this paper, the parameters used are choosen to ensure that the monostable region is the only one that is stable for the agent.
Mentions: The relative phase or phase difference, φ, represents the order parameter or collective variable that emerges from lower-level interactions of the two coupled oscillators, a and b are the coupling coefficients between the two oscillators, and Δω is the difference between their intrinsic frequencies. Despite its simplicity, this equation captures a wide range of self-organized phenomena. Different combinations of the control parameters a, b (or rather b/a) and Δω give rise to different collective behaviors. For example, when shifting the value of Δω while the values of a and b are held fixed, the system experiences phase transitions between three different modes of behavior: monostable, bistable and metastable (Figure 1).

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