Time-delay effects on dynamics of a two-actor conflict model

Rojas-Pacheco, A.; Obregón-Quintana, Bibiana; Liebovitch, Larry S.; Guzmán‐Vargas, L.

doi:10.1016/j.physa.2012.09.021

Cited by 10 publications

(10 citation statements)

References 15 publications

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“…Liebovitch et al [ 21 ] proposed a two-actor model based on the Gottman et al [ 22 ] mathematical model of the interaction between married couples and formulated appropriate equations and parameters to operationalize the concepts of the cooperative or competitive behavior of actors as described by Deutsch [ 4 , 6 ]. A later study [ 23 ] based on that model considered time delays in the interactions between the actors. Using a local stability analysis together with numerical simulations that study found important dynamic characteristics similar to those observed in real conflict situations.…”

Section: Introductionmentioning

confidence: 99%

The Dynamic Consequences of Cooperation and Competition in Small-World Networks

2015

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We present a study of the social dynamics among cooperative and competitive actors interacting on a complex network that has a small-world topology. In this model, the state of each actor depends on its previous state in time, its inertia to change, and the influence of its neighboring actors. Using numerical simulations, we determine how the distribution of final states of the actors and measures of the distances between the values of the actors at local and global levels, depend on the number of cooperative to competitive actors and the connectivity of the actors in the network. We find that similar numbers of cooperative and competitive actors yield the lowest values for the local and global measures of the distances between the values of the actors. On the other hand, when the number of either cooperative or competitive actors dominate the system, then the divergence is largest between the values of the actors. Our findings make new testable predictions on how the dynamics of a conflict depends on the strategies chosen by groups of actors and also have implications for the evolution of behaviors.

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Section: Introductionmentioning

confidence: 99%

The Dynamic Consequences of Cooperation and Competition in Small-World Networks

2015

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“…It can also be the back end for an interactive interface for policy makers to study the consequences of different interventions in the system. Extending previous mathematical models of networked systems [11][12][13][14][15] to analyze a CLD, we determine the value x i of each peace factor from:…”

Section: Mathematical Modelmentioning

confidence: 99%

Complexity analysis of sustainable peace: mathematical models and data science measurements

Liebovitch

Coleman²,

Bechhofer

et al. 2019

New J. Phys.

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Peace is not merely the absence of war and violence, rather 'positive peace' is the political, economic, and social systems that generate and sustain peaceful societies. Our international and multidisciplinary group is using physics inspired complex systems analysis methods to understand the factors and their interactions that together support and maintain peace. We developed causal loop diagrams and from them ordinary differential equation models of the system needed for sustainable peace. We then used that mathematical model to determine the attractors in the system, the dynamics of the approach to those attractors, and the factors and connections that play the most important role in determining the final state of the system. We used data science ('big data') methods to measure quantitative values of the peace factors from structured and unstructured (social media) data. We also developed a graphical user interface for the mathematical model so that social scientists or policy makers, can by themselves, explore the effects of changing the variables and parameters in these systems. These results demonstrate that complex systems analysis methods, previously developed and applied to physical and biological systems, can also be productively applied to analyze social systems such as those needed for sustainable peace.

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“…Páez-Hernández and Santillán [3] studied the effect that time delays produce in a mathematical model for the stretch reflex regulatory pathway. Rojas-Pacheco et al [4] studied time-delay effects on the dynamics of a two-actor conflict model.…”

Section: Time Delaysmentioning

confidence: 99%

Effects of Time Delays in a Dynamical Heart Model

Páez-Hernández¹,

Zamora-Gómez²,

Portillo-Díaz³

et al. 2014

JCCE

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Abstract:In this work, a dynamical model of the heartbeat is studied using nonlinear dynamics and considering the time delays inherent in the system. Two fixed points are associated to sustained oscillations which might be interpreted as the diastole and systole. These parameters are associated with blood flow in human body called arterial pressure and are very important in the cardio-vascular diagnostic.

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Time-delay effects on dynamics of a two-actor conflict model

Cited by 10 publications

References 15 publications

The Dynamic Consequences of Cooperation and Competition in Small-World Networks

The Dynamic Consequences of Cooperation and Competition in Small-World Networks

Complexity analysis of sustainable peace: mathematical models and data science measurements

Effects of Time Delays in a Dynamical Heart Model

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