New article on entraining chaotic dynamics

We show that it is possible for a participant to interactively control a chaotic system by entraining with its dynamics, with the effect that they become more regular while the participant becomes more chaotic.

This has implications both for researchers interested in controlling chaotic systems, and also for practitioners in movement rehabilitation.

Entraining chaotic dynamics: A novel movement sonification paradigm could promote generalization

Dobromir Dotov and Tom Froese

Tasks encountered in daily living may have instabilities and more dimensions than are sampled by the senses such as when carrying a cup of coffee and only the surface motion and overall momentum are sensed, not the fluid dynamics. Anticipating non-periodic dynamics is difficult but not impossible because mutual coordination allows for chaotic processes to synchronize to each other and become periodic. A chaotic oscillator with random period and amplitude affords being stabilized onto a periodic trajectory by a weak input if the driver incorporates information about the oscillator. We studied synchronization with predictable and unpredictable stimuli where the unpredictable stimuli could be non-interactive or interactive. The latter condition required learning to control a chaotic system. We expected better overall performance with the predictable but more learning and generalization with unpredictable interactive stimuli. Participants practiced an auditory-motor synchronization task by matching their sonified hand movements to sonified tutors: the Non-Interactive Predictable tutor (NI-P) was a sinusoid, the Non-Interactive Unpredictable (NI-U) was a chaotic system, the Interactive Unpredictable (I-U) was the same chaotic system with an added weak input from the participant’s movement. Different pre/post-practice stimuli evaluated generalization. Quick improvement was seen in NI-P. Synchronization, dynamic similarity, and causal interaction increased with practice in I-U but not in NI-U. Generalization was seen for few pre-post stimuli in NI-P, none in NI-U, and most stimuli in I-U. Synchronization with novel chaotic dynamics is challenging but mutual interaction enables the behavioral control of such dynamics and the practice of complex motor skills.


Psychological study on chaos control

Dobri Dotov and I have published an extended abstract in the Proceedings of the Artificial Life Conference 2018 about the study that he realized at UNAM. We suggest that the results have implications for how we should think about how to stabilize the behavior of complex adaptive systems with which we can interact.

We will present this work at the ALIFE conference in Tokyo as part of the special session on “ALife and Society: Transcending the artificial-natural divide”.

Mutual synchronization and control between artificial chaotic system and human

Dobromir Dotov and Tom Froese

Dexterous assistive devices constitute one of the frontiers for hybrid human-machine systems. Manipulating unstable systems requires task-specific anticipatory dynamics. Learning this dynamics is more difficult when tasks, such as carrying liquid or riding a horse, produce unpredictable, irregular patterns of feedback and have hidden dimensions not projected as sensory feedback. We addressed the issue of coordination with complex systems producing irregular behaviour, with the assumption that mutual coordination allows for non-periodic processes to synchronize and in doing so to become regular. Chaos control gives formal expression to this: chaos can be stabilized onto periodic trajectories provided that the structure of the driving input takes into account the causal structure of the controlled system.

Can we learn chaos control in a sensorimotor task? Three groups practiced an auditory-motor synchronization task by matching their continuously sonified hand movements to sonified tutors: a sinusoid served as a Non-Interactive Predictable tutor (NIP), a chaotic system stood for a Non-Interactive Unpredictable tutor (NI-U), and the same system weakly driven by the participant’s movement stood for an Interactive Unpredictable tutor (I-U). We found that synchronization, dynamic similarity, and causal interaction increased with practice in I-U. Our findings have implications for current efforts to find more adequate ways of controlling complex adaptive systems.