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.
Oscillatory phenomena are ubiquitous in nature and have become particularly relevant for the study of brain and behaviour. One of the simplest, yet explanatorily powerful, models of oscillatory coordination dynamics is the the HKB (Haken-Kelso-Bunz) model. The metastable regime described by the HKB equation has been hypothesized to be the signature of brain oscillatory dynamics underlying sensorimotor coordination. Despite evidence supporting such a hypothesis, to our knowledge there are still very few models (if any) where the HKB equation generates spatially situated behaviour and, at the same time, has its dynamics modulated by the behaviour it generates (by means of the sensory feedback resulting from body movement). This work presents a computational model where the HKB equation controls an agent performing a simple gradient climbing task and shows i) how different metastable dynamical patterns in the HKB equation are generated and sustained by the continuous interaction between the agent and its environment; and ii) how the emergence of functional metastable patterns in the HKB equation -i.e. patterns that generate gradient climbing behaviour -depends not only on the structure of the agent's sensory input but also on the coordinated coupling of the agent's motor-sensory dynamics. This work contributes to Kelso's theoretical framework and also to the understanding of neural oscillations and sensorimotor coordination.
Synchronous oscillations have become a widespread hypothetical “mechanism” to explain how brain dynamics give rise to neural functions. By focusing on synchrony one leaves the phase relations during moments of desynchronous oscillations either without a clear functional role or with a secondary role such as a transition between functionally “relevant” synchronized states. In this work, rather than studying synchrony we focus on desynchronous oscillations and investigate their functional roles in the context of a sensorimotor coordination task. In particular, we address the questions: a) how does the informational content of the sensorimotor activity present in a complete dynamical description of phase relations change as such a description is reduced to the dynamics of synchronous oscillations? and b) to what extent are desynchronous oscillations as causally relevant as synchronous ones to the generation of functional sensorimotor coordination? These questions are addressed with a model of a simulated agent performing a functional sensorimotor coordination task controlled by an oscillatory network. The results suggest that: i) desynchronized phase relations carry as much information about sensorimotor activity as synchronized phase relations; and ii) phase relations between oscillators with near-zero frequency difference carry a relatively higher causal relevance than the rest of the phase relations to the sensorimotor coordination; however, overall a privileged functional causal contribution can not be attributed to either synchronous or desynchronous oscillations.
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