Necessary and sufficient conditions for asymptotic swarm stability of high order swarm systems

2010 ◽  
Author(s):  
Ning Cai ◽  
Jianxiang Xi ◽  
Yisheng Zhong
Keyword(s):  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

The M/M/1 queue with mass exodus and mass arrivals when empty

1997 ◽  
Vol 34 (01) ◽  
pp. 192-207 ◽  
Author(s):  
Anyue Chen ◽  
Eric Renshaw
Keyword(s):  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Positive Recurrence ◽  
Powerful Technique ◽  
Resolvent Approach ◽  
Necessary And Sufficient ◽  
Direct Attack

An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

scholarly journals High-Order Iterative Methods for the DMP Inverse

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Xiaoji Liu ◽  
Naping Cai
Keyword(s):  
Error Estimate ◽  
Iterative Methods ◽  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Sufficient Conditions For Convergence ◽  
Necessary And Sufficient ◽  
High Order Iterative Methods

We investigate two iterative methods for computing the DMP inverse. The necessary and sufficient conditions for convergence of our schemes are considered and the error estimate is also derived. Numerical examples are given to test the accuracy and effectiveness of our methods.

scholarly journals Collective Coordination of High-Order Dynamic Multiagent Systems Guided by Multiple Leaders

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Xin-Lei Feng ◽  
Ting-Zhu Huang ◽  
Jin-Liang Shao
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Second Order ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Multiple Leaders ◽  
Theoretical Results

For second-order and high-order dynamic multiagent systems with multiple leaders, the coordination schemes that all the follower agents flock to the polytope region formed by multiple leaders are considered. Necessary and sufficient conditions which the follower agents can enter the polytope region by the leaders are obtained. Finally, numerical examples are given to illustrate our theoretical results.

scholarly journals Fixed Point and Newton’s Methods in the Complex Plane

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
François Dubeau ◽  
Calvin Gnang
Keyword(s):  
Fixed Point ◽  
Complex Plane ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Newton's Methods

We revisit the necessary and sufficient conditions for linear and high order of convergence of fixed point and Newton’s methods in the complex plane. Schröder’s processes of the first and second kind are revisited and extended. Examples and numerical experiments are included.

The M/M/1 queue with mass exodus and mass arrivals when empty

1997 ◽  
Vol 34 (1) ◽  
pp. 192-207 ◽  
Author(s):  
Anyue Chen ◽  
Eric Renshaw
Keyword(s):  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Positive Recurrence ◽  
Powerful Technique ◽  
Resolvent Approach ◽  
Necessary And Sufficient ◽  
Direct Attack

An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Sign in / Sign up

Export Citation Format

Share Document