Theorem on Conflict for a Pair of Stochastic Vectors

Koshmanenko, V. D.

doi:10.1023/b:ukma.0000010167.63115.37

Cited by 26 publications

(44 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that the mathematical model of the conflict triad is based on the notion of the dynamical conflict system introduced in [4][5][6][7][8][9]12]. Among other deep theoretical investigations that influenced our constructions, we mention the results of [14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Model of a dynamical system of a conflict triad

Koshmanenko¹,

Самойленко²

2011

Nonlinear Oscill

Self Cite

View full text Add to dashboard Cite

We investigate a model of a dynamical system of a conflict triad that describes the interaction between the substances of the natural triad: biological populations (life), environment (living resources), and negative influences (infection). The main phases of coexistence of the substances of the triad are established: the equilibrium dynamical state (a stable fixed point), cyclic attractors, periodically oscillating trajectories, and evolutions close to chaotic ones. The existence of bifurcation points and thresholds of transitions between phases are shown for specific models.

show abstract

Section: Introductionmentioning

confidence: 99%

Model of a dynamical system of a conflict triad

Koshmanenko¹,

Самойленко²

2011

Nonlinear Oscill

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the case of finitely many conflict positions, we have p, r ∈ R n , n < ∞. If the number of conflict positions is arbitrary, then we assume that p, r ∈ l 1 . The values of the coordinates p i and r i are interpreted as the independent probabilities of occupying the ith conflict position by the corresponding opponents.…”

Section: Introductionmentioning

confidence: 99%

“…The notion of conflict composition for stochastic vectors with a finite number of coordinates and the coupling coefficient α = 1 was first introduced in [1] (see also [2,3]). In the present paper, the notion of conflict composition for indestructible opponents with repulsion effect is generalized to the case of an arbitrary value of the coupling coefficient 0 < α ≤ 1.…”

Section: Introductionmentioning

confidence: 99%

“…In the case α = 1, the conflict composition is well defined if the initial vectors satisfy the condition 1 = (p, r). It should be noted that the value of p (1) i is proportional to the product of the initial probability p i of occupying the ith position and the probability of the absence of the opponent at this position (the last quantity is taken with regard for the coefficient of interaction α). The quantity r (1) i is interpreted by analogy.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Properties of the Limit States of a Dynamical Conflict System

2004

Self Cite

View full text Add to dashboard Cite

We study the properties of a dynamical system generated by a nonlinear conflict composition for indestructible opponents with an arbitrary (including infinite) number of conflict positions and a coupling coefficient α, 0 < α ≤ 1. We prove the existence of limit invariant states and give a complete description of their structure in terms of initial states. In the cases of two and three conflict positions, we give a geometric interpretation.

show abstract

“…One case is that there are two rows, It must be emphasized that the limiting distribution of the matrix strongly depends on the initial conditions. Koshmanenko shows such phenomena in a purely mathematical way for two opponents (Koshmanenko, 2003(Koshmanenko, , 2004. However in the next section they are demonstrated through a generalized simulation so that more complicated situations may be dealt with.…”

Section: Game Theory To the Conflict Modelmentioning

confidence: 99%

Segregation through Conflict

Khan¹,

Takahashi²

2013

AASoci

View full text Add to dashboard Cite

This paper begins by introducing the game theory to explain how an institution emerges. It then goes on to employ a conflict model, using the probability distribution introduced by Koshmanenko, to show how institutions emerge through mathematical formation. This is followed by a consideration of the authors' development of a segregation simulation based on this conflict theory. An institution is defined as the equilibrium achieved through the segregation of conflicting groups (for example groups differing according to "race", or language, education or income level among other factors). A simulation is made explaining how equilibrium is reached through changing probability. This simulation also shows the dynamics of an emerging new order.

show abstract

Theorem on Conflict for a Pair of Stochastic Vectors

Cited by 26 publications

References 5 publications

Model of a dynamical system of a conflict triad

Model of a dynamical system of a conflict triad

Properties of the Limit States of a Dynamical Conflict System

Segregation through Conflict

Contact Info

Product

Resources

About