Synchronized states and multistability in a random network of coupled discontinuous maps
Mayurakshi Nag1, Swarup Poria1
1Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata 700 009, India.
Chaos (Woodbury, N.Y.)
|September 3, 2015
Summary
This study reveals that dynamic random connections in coupled chaotic maps lead to synchronized multistability. The network synchronizes to different unstable fixed points, influenced by map discontinuity and rewiring probability.
Area of Science:
- Complex Networks
- Chaos Theory
- Nonlinear Dynamics
Background:
- Coupled chaotic maps are fundamental in understanding complex system dynamics.
- Synchronization phenomena in networks are crucial for information processing and emergent behaviors.
- Unstable fixed points in local maps pose challenges for network synchronization.
Purpose of the Study:
- To investigate the synchronization behavior of coupled chaotic discontinuous maps on a ring network with dynamic random connections.
- To explore the emergence of synchronized multistability and its dependence on network topology and map properties.
- To identify bifurcations and determine the parameter space for synchronized states.
Main Methods:
- Simulating coupled chaotic discontinuous maps on a ring network with dynamic random rewiring.
- Analyzing the stability of fixed points under random rewiring.
- Investigating the influence of map discontinuity length, coupling strength, and rewiring probability on synchronization patterns.
Main Results:
- Random rewiring stabilizes one of two strongly unstable fixed points of the local map.
- The network exhibits synchronized multistability, synchronizing to different unstable fixed points based on initial conditions.
- Synchronized fixed points and periodic orbits are observed, influenced by coupling strength and local map parameters.
- Period subtracting bifurcation is identified with respect to coupling strength.
- The range of coupling strength for synchronized multistable spatiotemporal fixed points is determined and depends on dynamic rewiring probability and local map characteristics.
Conclusions:
- Dynamic random connections induce synchronized multistability in coupled chaotic discontinuous map networks.
- The discontinuity of the local map plays a critical role in generating diverse synchronized states.
- Network synchronization is controllable through coupling strength, map parameters, and rewiring dynamics.
Related Concept Videos
01:25Multimachine Stability
625
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:
625
01:24BIBO stability of continuous and discrete -time systems
1.1K
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
1.1K
01:14The Entropy as a State Function
100
Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
100
01:10Entropy Change in Reversible Processes
3.4K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.4K
01:27State Space Representation
724
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Consider an RLC circuit, a...
724
01:19Limits with Oscillating Discontinuities
622
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
622