Temporal Patterns in Non-Linear Oscillators
The overall goal of this research is to understand the mechanisms that underlie spatial and temporal pattern formation in weakly coupled oscillator networks. The evolution of these patterns helps to shed light on the dynamics of information processing. To this end, we have developed a method that monitors and analyzes temporal interdependencies between weakly interacting non-identical systems. Causal relationships between the elements in the networks are typical features that are captured by this method. We have investigated the behavior of this measure by using it to study the evolution of asymmetrical temporal relationships between two coupled Rössler oscillators as these oscillators are versatile dynamical non-linear oscillators that can display a wide range of temporal behavior. We are currently using this measure to study temporal patterns in networks of coupled Rössler oscillators as the network topology is modified.
Featured Results
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The causal entropy between two Rössler oscillators. a is the coupling strength, a is the control parameter. For uncoupled oscillators, both CEs are high. For coupled identical oscillators, both CEs are low. Finally, for coupled heterogeneous oscillators, one CE is low while the other is high, demonstrating the causal ordering between them. |
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The causal entropy difference between pairs of oscillators with the indicated control parameters. Except for identical oscillators, the causal entropy difference details the leader-follower relationship between each pair of oscillators. |
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