Particle swarm stability: a theoretical extension using the non-stagnate distribution assumption

@article{Cleghorn2017ParticleSS,
  title={Particle swarm stability: a theoretical extension using the non-stagnate distribution assumption},
  author={Christopher Wesley Cleghorn and Andries Petrus Engelbrecht},
  journal={Swarm Intelligence},
  year={2017},
  volume={12},
  pages={1-22}
}
This paper presents an extension of the state of the art theoretical model utilized for understanding the stability criteria of the particles in particle swarm optimization algorithms. Conditions for order-1 and order-2 stability are derived by modeling, in the simplest case, the expected value and variance of a particle’s personal and neighborhood best positions as convergent sequences of random variables. Furthermore, the condition that the expected value and variance of a particle’s personal… 
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