Related papers: Early warning signals for phase transitions in net…
Bank crisis is challenging to define but can be manifested through bank contagion. This study presents a comprehensive framework grounded in nonlinear time series analysis to identify potential early warning signals (EWS) for impending…
Early-warning indicators (increase of autocorrelation and variance) are commonly applied to time series data to try and detect tipping points of real-world systems. The theory behind these indicators originates from approximating the…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional…
The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between…
Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum…
In several natural and engineering systems, changes in control parameters can trigger bifurcations that lead to sustained or growing periodic oscillations, indicating the onset of oscillatory instabilities. Such emergent behaviour often…
We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections $P(k)$. The theory shows that the critical behavior depends in a crucial way on the form of $P(k)$ and differs strongly…
We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently…
The existence of explosive phase transitions in random (Erd\H os R\'enyi-type) networks has been recently documented by Achlioptas et al.\ [Science {\bf 323}, 1453 (2009)] via simulations. In this Letter we describe the underlying mechanism…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…