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\label{sec:metastability} Metastability in animal behavior

The usual way to model metastability is to divide the state space into non-overlapping partitions and associate an exponentially small transition probability between the partitions. In biology, such picture is not always accurate. It is common to assume that the metastability happens in the transition between potentials that are associated with same state space. An obvious example is given by an animal that forages in an arena. It is clear from an observer that when the animal interacts with the wall (e.g., hits the wall), it changes its dynamics, although still moving within the same arena. An observer would characterize such change as transition between different animal behaviors. It is then natural to assume that the transition between animal behaviors corresponds to transition between metastable states. Give some example for development and evolution.
Examples of metastability from physics / non linear dynamics and how the definition differ concretely from biology
It is clear from this picture that there at least four time scales to consider when trying to understand animal behavior. The fastest time scale is the sum of several factor that are modeled by random noise. The dynamics of the animal in the phase space, represents the second fastest time scale. The third time scale is given by the change in the parameters that controls the the dynamics of the animal. This change is driven by the interaction between the animal dynamics and the constraints of the system that represents the slowest time scale.
The importance of the experimental observation time in ”understanding” behavior”
Behavior can be regarded as constrained dynamics with memory. Our proposed model thus take into account constraints, dynamics and memory. Constraints can be regarded as an abstract geometrical object that delineate the boundaries spanned by the dynamics. The constraints should be considered only as reflecting space but within our framework any constraints (both environmental and biological ) can be mapped onto a high dimensional geometrical object. The model is out of thermodynamical equilibrium and non-markovian
The establishment of an Ising - like model for behavior. Ising models have been successfully used to understand universal properties in many classes of biological systems from gene networks to neuronal networks. A similar approach with behavior is lacking that focuses on elucidating universal principles of behavior.
Drawing from Cybernetic principles , behavior can be broadly defined / understood as a feedback control system. In our case, it is the feedback between the dynamics and constraints that shapes behavior to navigate across different and select appropriate affordances. Affordances can be defined as a potential action that is made possible to an agent by the environment around it. While affordances are defined with respect to an agent’s individual capabilities (e.g., a tree branch might have a ‘ walkability affordance for a monkey, not necessarily for a sedentary man), they are objective in the sense that they do not depend on whether the agent perceives them, attends to them, or chooses to act on them, and can be recognized by anyone familiar with the agent’s motor repertoire. The affordance landscape in our model is the set of all possible actions defined over the constraints on which the particle / agent is acting.
Contrast with energy landscape , energy landscape is static but the affordance landscape is dynamic owing to the existence of a feedback loop.
What is called affordance in the literature (Gibson, Jakob Van Uekell, …) refers to all action possibilities in the environment in relation to the agent. In our model , the parameter space of a represents the affordances (which control the possible behavior of the animal in the environment in a closed loop fashion ) .
There is recent resurgence interest in closed loop approaches to understanding the brain not only as an experimental approach but as a framework to understand behavior.