Multidimensional complex systems – transition distributions as a resilience measure

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University of Alabama Libraries

Complex networks can be observed in many areas ranging from ecological and biological to technical systems. Complex systems have many interacting components which make their dynamics non-linear. This makes it difficult to calculate important properties of the system such as resilience. The resilience of a system is how persistent the system is against external perturbations. Node centrality determines the importance that a node plays in the effective working of a network. The effect node centrality plays on the transition taking place was explored. Resilience has been defined based on the fraction of nodes that needs to be removed before the system fails. The fraction of nodes to be removed have been calculated statistically by calculating the centroid of the transition distribution. The logic used for defining resilience this way was that if the system transitions into the unwanted lower equilibrium state after a small perturbation it has a lower resilience than the system which transitions to that state after greater perturbation. The values of resilience obtained from the transition distribution agree with the trend in resilience shown by the effective control parameter, β_eff. It was concluded that the node centrality plays an important part in the transition distribution and hence it is important to identify the important or the most central nodes in the system also known as ‘hubs’. The current work proposes to lay a foundation to predict the dynamics of the same complex network with the help of Artificial Neural Networks. The recurrent Artificial Neural Networks have been trained using the data obtained by solving the set of non-linear ordinary differential equations which describe the spatial and temporal dynamics of the system. These equations have been solved numerically by a self-developed solver based on the Runge Kutta 4 algorithm. The architecture chosen for the neural network was the Simple Recurrent Neural Network. The Levenberg-Marquardt algorithm was used for training the neural network.

Electronic Thesis or Dissertation
Aerospace engineering, Engineering, Statistical physics