Related Experiment Video
Updated: Apr 29, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
708
Network risk and forecasting power in phase-flipping dynamical networks.
B Podobnik1, A Majdandzic2, C Curme2
1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Faculty of Civil Engineering, University of Rijeka, 51000 Rijeka, Croatia and Zagreb School of Economics and Management, 10000 Zagreb, Croatia and Faculty of Economics, University of Ljubljana, 1000 Ljubljana, Slovenia.
Summary
This study models network failures and recovery, revealing how random recovery processes impact network stability and risk. We developed methods to quantify network risk, applicable to economic and traffic systems.
Area of Science:
- Network Science
- Complex Systems
- Dynamical Systems
Background:
- Real-world networks exhibit volatile behavior due to node and link failures.
- Understanding network resilience under dynamic conditions is crucial for various applications.
Purpose of the Study:
- To model phase-flipping dynamics in scale-free networks with stochastic node and link failures.
- To investigate the impact of recovery process stochasticity on network stability.
- To develop risk estimators for network resilience.
Main Methods:
- Analysis of a phase-flipping dynamical scale-free network model.
- Stochastic investigation of recovery parameters.
- Derivation of higher moments for active node and link fractions (fn(t), fℓ(t)).
- Definition of network risk estimators.
- Analysis of hysteresis in node fraction correlations.
Main Results:
- Quantified the probability of limited node and link failures (q%).
- Derived higher moments of active fractions, fn(t) and fℓ(t).
- Identified hysteresis in fn(t) correlations due to node failures.
- Derived conditional probabilities for phase-flipping events.
- Demonstrated applicability to economic and traffic networks.
Conclusions:
- The model provides insights into network resilience and risk under dynamic failure and recovery processes.
- Stochasticity in recovery significantly influences phase-flipping dynamics.
- The developed estimators offer a quantitative measure of network risk.
Related Concept Videos
01:21Power System Three-Phase Short Circuits
741
Determining the subtransient fault current in a power system involves representing transformers by their leakage reactances, transmission lines by their equivalent series reactances, and synchronous machines as constant voltage sources behind their subtransient reactances. In this analysis, certain elements are excluded, such as winding resistances, series resistances, shunt admittances, delta-Y phase shifts, armature resistance, saturation, saliency, non-rotating impedance loads, and small...
741
01:25Multimachine Stability
695
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
695
01:24Fast Decoupled and DC Powerflow
961
The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
961
01:15Power in a Three-Phase Circuit
750
Three-phase systems have two configurations: the wye and delta. A star configuration can be three or four wires; in a delta configuration, the components are connected in a closed loop. Instantaneous power refers to the power value at a precise moment, and in a balanced three-phase system, it is constant. This is because the sum of the instantaneous powers in the three phases remains steady over time, despite individual fluctuations, due to the symmetry and phase relationship. The total...
750
01:24Bus Impedance Matrix
621
Calculating subtransient fault currents for three-phase faults in an N-bus power system involves using the positive-sequence network. When a three-phase short circuit occurs at a specific bus, the analysis uses the superposition method to evaluate two separate circuits.
In the first circuit, all machine voltage sources are short-circuited, leaving only the prefault voltage source at the fault location. The positive-sequence bus impedance matrix can be determined by solving the nodal equations,...
In the first circuit, all machine voltage sources are short-circuited, leaving only the prefault voltage source at the fault location. The positive-sequence bus impedance matrix can be determined by solving the nodal equations,...
621
01:23Maximum Power Flow and Line Loadability
777
The maximum power flow for lossy transmission lines is derived using ABCD parameters in phasor form. These parameters create a matrix relationship between the sending-end and receiving-end voltages and currents, allowing the determination of the receiving-end current. This relationship facilitates calculating the complex power delivered to the receiving end, from which real and reactive power components are derived.
777