Chaos from nonlinear Markov processes: Why the whole is different from the sum of its parts

2009 ◽  
Vol 388 (19) ◽  
pp. 4241-4247 ◽  
Author(s):  
T.D. Frank
Keyword(s):  
Markov Processes ◽  
Nonlinear Markov Processes

Nonlinear Markov Processes and Kinetic Equations

2009 ◽  
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Markov Processes ◽  
Kinetic Equations ◽  
Nonlinear Markov Processes

scholarly journals On invariant measures of nonlinear Markov processes

1993 ◽  
Vol 6 (4) ◽  
pp. 385-406 ◽  
Author(s):  
N. U. Ahmed ◽  
Xinhong Ding
Keyword(s):  
Markov Process ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Invariant Measures ◽  
Nonlinear Markov Processes

We consider a nonlinear (in the sense of McKean) Markov process described by a stochastic differential equations in Rd. We prove the existence and uniqueness of invariant measures of such process.

scholarly journals Local stability of Kolmogorov forward equations for finite state nonlinear Markov processes

2015 ◽  
Vol 20 (0) ◽  
Author(s):  
Amarjit Budhiraja ◽  
Paul Dupuis ◽  
Markus Fischer ◽  
Kavita Ramanan
Keyword(s):  
Markov Processes ◽  
Local Stability ◽  
Finite State ◽  
Nonlinear Markov Processes ◽  
Forward Equations ◽  
Kolmogorov Forward Equations

MICRO-DYNAMIC ASSOCIATED WITH TWO-STATE NONLINEAR MARKOV PROCESSES: WITH AN APPLICATION TO FREE RECALL

2011 ◽  
Vol 10 (01) ◽  
pp. 41-58 ◽  
Author(s):  
T. D. FRANK ◽  
T. RHODES
Keyword(s):  
Free Recall ◽  
Markov Processes ◽  
Dynamic Models ◽  
Mean Field ◽  
Variational Calculus ◽  
State Model ◽  
Recall Data ◽  
Nonlinear Markov Processes ◽  
Many Body Systems ◽  
Two State Model

We examine the relationship between time-discrete nonlinear Markov processes defined in terms of nonlinear Markov chains and corresponding micro-dynamic models describing many-body systems composed of a finite number of units interacting with each other via a mean field. To this end, we consider a two-state model and examine appropriately defined measures for attractor strength and noise amplitude using variational calculus. We focus on a two-state model and demonstrate an application to free recall data from 8 participants.

Relationship of fluctuations and transport for nonlinear Markov processes

1986 ◽  
Vol 33 (6) ◽  
pp. 4307-4311 ◽  
Author(s):  
James W. Dufty ◽  
J. Javier Brey ◽  
M. Cristina Marchetti
Keyword(s):  
Markov Processes ◽  
Nonlinear Markov Processes ◽  
Relationship Of

scholarly journals Nonlinear Markov processes in big networks

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Quan-Lin Li
Keyword(s):  
Markov Process ◽  
Fixed Points ◽  
Markov Processes ◽  
Continuous Time ◽  
Manufacturing Systems ◽  
Stochastic Systems ◽  
Time Block ◽  
Nonlinear Markov Processes ◽  
Nonlinear Markov Process ◽  
Block Structured

AbstractBig networks express multiple classes of large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to constructing a broad class of nonlinear continuous-time block-structured Markov processes, which can be used to deal with many practical stochastic systems. Firstly, a nonlinear Markov process is derived from a large number of big networks with weak interactions, where each big network is described as a continuous-time block-structured Markov process. Secondly, some effective algorithms are given for computing the fixed points of the nonlinear Markov process by means of the UL-type RG-factorization. Finally, the Birkhoff center, the locally stable fixed points, the Lyapunov functions and the relative entropy are developed to analyze stability or metastability of the system of weakly interacting big networks, and several interesting open problems are proposed with detailed interpretation. We believe that the methodology and results given in this paper can be useful and effective in the study of big networks.

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