Noisy consensus dynamics in windmill-type graphs

2020 ◽  
Vol 30 (12) ◽  
pp. 123131
Author(s):  
Weigang Sun ◽  
Yifan Li ◽  
Suyu Liu
Keyword(s):  
Consensus Dynamics

scholarly journals Sparse stabilization and control of alignment models

2014 ◽  
Vol 25 (03) ◽  
pp. 521-564 ◽  
Author(s):  
Marco Caponigro ◽  
Massimo Fornasier ◽  
Benedetto Piccoli ◽  
Emmanuel Trélat
Keyword(s):  
Policy Maker ◽  
Research Direction ◽  
Fundamental Question ◽  
Self Organization ◽  
Group Consensus ◽  
Future Developments ◽  
Consensus Dynamics ◽  
Time Optimal ◽  
And Control ◽  
Mathematical Justification

Starting with the seminal papers of Reynolds (1987), Vicsek et al. (1995), Cucker–Smale (2007), there has been a lot of recent works on models of self-alignment and consensus dynamics. Self-organization has so far been the main driving concept of this research direction. However, the evidence that in practice self-organization does not necessarily occur (for instance, the achievement of unanimous consensus in government decisions) leads to the natural question of whether it is possible to externally influence the dynamics in order to promote the formation of certain desired patterns. Once this fundamental question is posed, one is also faced with the issue of defining the best way of obtaining the result, seeking for the most "economical" way to achieve a certain outcome. Our paper precisely addressed the issue of finding the sparsest control strategy in order to lead us optimally towards a given outcome, in this case the achievement of a state where the group will be able by self-organization to reach an alignment consensus. As a consequence, we provide a mathematical justification to the general principle according to which "sparse is better": in order to achieve group consensus, a policy maker not allowed to predict future developments should decide to control with stronger action the fewest possible leaders rather than trying to act on more agents with minor strength. We then establish local and global sparse controllability properties to consensus. Finally, we analyze the sparsity of solutions of the finite time optimal control problem where the minimization criterion is a combination of the distance from consensus and of the ℓ1-norm of the control. Such an optimization models the situation where the policy maker is actually allowed to observe future developments. We show that the lacunarity of sparsity is related to the codimension of certain manifolds in the space of cotangent vectors.

Design of Attack-Resilient Consensus Dynamics: A Game-Theoretic Approach

2019 ◽  
Author(s):  
Mohammad Pirani ◽  
Ehsan Nekouei ◽  
Seyed Mehran Dibaji ◽  
Henrik Sandberg ◽  
Karl Henrik Johansson
Keyword(s):  
Theoretic Approach ◽  
Consensus Dynamics ◽  
Game Theoretic ◽  
Game Theoretic Approach

scholarly journals Explosive transitions induced by interdependent contagion-consensus dynamics in multiplex networks

2019 ◽  
Vol 99 (6) ◽  
Author(s):  
D. Soriano-Paños ◽  
Q. Guo ◽  
V. Latora ◽  
J. Gómez-Gardeñes
Keyword(s):  
Multiplex Networks ◽  
Consensus Dynamics

Influence of Leaders on Mean Square Consentability in Biologically-Inspired Stochastic Networks

2011 ◽  
Author(s):  
Nicole Abaid ◽  
Maurizio Porfiri
Keyword(s):  
Collective Behavior ◽  
Information Exchange ◽  
Stochastic Networks ◽  
Closed Form Expression ◽  
Convergence Factor ◽  
Form Expression ◽  
Consensus Protocol ◽  
Biologically Inspired ◽  
Size Number ◽  
Consensus Dynamics

In this work, we study a discrete-time consensus protocol for a group of agents which communicate over a class of stochastically switching networks inspired by fish schooling. The network model incorporates the phenomenon of numerosity that has a prominent role on the collective behavior of animal groups by defining the individuals’ perception of numbers. The agents comprise leaders, which share a common state, and followers, which update their states based on information exchange among neighboring agents. We write a closed form expression for the asymptotic convergence factor of the protocol, which measures the decay rate of disagreement among the followers’ and the leaders’ states. Numerical simulations are conducted to validate analytical results and illustrate the consensus dynamics as a function of the group size, number of leaders in the group, and the numerosity.

scholarly journals Multibody interactions and nonlinear consensus dynamics on networked systems

2020 ◽  
Vol 101 (3) ◽  
Author(s):  
Leonie Neuhäuser ◽  
Andrew Mellor ◽  
Renaud Lambiotte
Keyword(s):  
Networked Systems ◽  
Consensus Dynamics

Shapley and superShapley aggregation emerging from consensus dynamics in the multicriteria Choquet framework

2020 ◽  
Vol 43 (2) ◽  
pp. 583-611 ◽  
Author(s):  
Silvia Bortot ◽  
Ricardo Alberto Marques Pereira ◽  
Anastasia Stamatopoulou
Keyword(s):  
Consensus Dynamics
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