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As put forward by neuroscientists, the mechanisms of consciousness can be elucidated by revealing correlations between neural dynamics and specific conscious percepts. Recently, I have elaborated on the mathematical formulation for a system…
Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…
This paper begins with a dynamical model that was obtained by applying a machine learning technique (FJet) to time-series data; this dynamical model is then analyzed with Lie symmetry techniques to obtain constants of motion. This analysis…
We consider the prisoner's dilemma being played repeatedly on a dynamic network, where agents may choose their actions as well as their co-players. This leads to co-evolution of network structure and strategy patterns of the players.…
Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this…
Nonlinear dynamical systems such as Lorenz63 equations are known to be chaotic in nature and sensitive to initial conditions. As a result, a small perturbation in the initial conditions results in deviation in state trajectory after a few…
Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information…
Shared Memory is a mechanism that allows several processes to communicate with each other by accessing -- writing or reading -- a set of variables that they have in common. A Consistency Model defines how each process observes the state of…
How spiking neuronal networks encode memories in their different time and spatial scales constitute a fundamental topic in neuroscience and neuro-inspired engineering. Much attention has been paid to large networks and long-term memory, for…
Biological systems have the unique ability to self-organize and generate autonomous motion and work. Motivated by this, we investigate a 2D model colloidal network that can repeatedly transition between disordered states of low connectivity…
Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…
We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…
We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random inter-unit connections reflect long-range interactions. When sufficiently…
Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise.…
A coupled oscillator network may be able to perform an energy-efficient associative memory operation. However, its realization has been difficult because inhomogeneities unavoidably arise among the oscillators during fabrication and lead to…
Cluster synchronization is of paramount importance for the normal functioning of numerous technological and natural systems. Deviations from normal cluster synchronization patterns are closely associated with various malfunctions, such as…
The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states,…
Combinatorial threshold-linear networks (CTLNs) are a special class of recurrent neural networks whose dynamics are tightly controlled by an underlying directed graph. Recurrent networks have long been used as models for associative memory…
Transitions from reversible to irreversible or fluctuating states above a critical density and shear amplitude have been extensively studied in non-thermal cyclically sheared suspensions and amorphous solids. Here, we propose that the same…
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…