COMPUTATIONAL UNFOLDING OF DOUBLE-CUSP MODELS OF OPINION FORMATION

1991 ◽  
Vol 01 (02) ◽  
pp. 417-430 ◽  
Author(s):  
RALPH ABRAHAM ◽  
ALEXANDER KEITH ◽  
MATTHEW KOEBBE ◽  
GOTTFRIED MAYER-KRESS
Keyword(s):  
Computational Study ◽  
Opinion Dynamics ◽  
Chaotic Attractors ◽  
Cusp Catastrophe ◽  
Opinion Formation ◽  
Catastrophe Model ◽  
Model Study ◽  
Periodic Attractors ◽  
Potential Applications ◽  
Democratic Nation

In 1975, Isnard and Zeeman proposed a cusp catastrophe model for the polarization of a social group, such as the population of a democratic nation. Ten years later, Kadyrov combined two of these cusps into a model for the opinion dynamics of two "nonsocialist" nations. This is a nongradient dynamical system, more general than the double-cusp catastrophe studied by Callahan and Sashin [1987]. Here, we present a computational study of the nongradient double cusp, in which the degeneracy of Kadyrov's model is unfolded in codimension eight. Also, we develop a discrete-time cusp model, study the corresponding double cusp, establish its equivalence to the continuous-time double cusp, and discuss some potential applications. We find bifurcations for multiple critical-point attractors, periodic attractors, and (for the discrete case) bifurcations to quasiperiodic and chaotic attractors.

Opinion Dynamics Optimization by Varying Susceptibility to Persuasion via Non-Convex Local Search

2021 ◽  
Vol 16 (2) ◽  
pp. 1-34
Author(s):  
Rediet Abebe ◽  
T.-H. HUBERT Chan ◽  
Jon Kleinberg ◽  
Zhibin Liang ◽  
David Parkes ◽  
...  
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Iterative Process ◽  
Large Scale ◽  
Opinion Dynamics ◽  
Theoretical Models ◽  
Global Optimum ◽  
Local Optimum ◽  
Opinion Formation ◽  
Long Line

A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

scholarly journals Cusp Catastrophe Model

2014 ◽  
Vol 63 (3) ◽  
pp. 211-220 ◽  
Author(s):  
Ding-Geng (Din) Chen ◽  
Feng Lin ◽  
Xinguang (Jim) Chen ◽  
Wan Tang ◽  
Harriet Kitzman
Keyword(s):  
Cusp Catastrophe ◽  
Catastrophe Model ◽  
Cusp Catastrophe Model

Comparison of P- and As-core-modified porphyrins with the parental porphyrin: a computational study

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Aleksey E. Kuznetsov
Keyword(s):  
Computational Study ◽  
Electron Delocalization ◽  
Energy Structure ◽  
Frontier Molecular Orbitals ◽  
The Core ◽  
Potential Applications ◽  
Noticeable Reduction ◽  
Internal Electron ◽  
Porphyrin Core ◽  
Homo Lumo

Abstract The first comparative DFT (B3LYP/6-31G*) study of the Zn-porphyrin and its two derivatives, ZnP(P)4 and ZnP(As)4, is reported. For all three species studied, ZnP, ZnP(P)4 and ZnP(As)4, the singlet was calculated to be the lowest-energy structure and singlet-triplet gap was found to decrease from ca. 41—42 kcal/mol for N to ca. 17—18 kcal/mol for P and to ca. 10 kcal/mol for As. Both ZnP(P)4 and ZnP(As)4 were calculated to attain very pronounced bowl-like shapes. The frontier molecular orbitals (MOs) of the core-modified porphyrins are quite similar to the ZnP frontier MOs. For the HOMO-2 of the core-modified porphyrins due to the ZnP(P)4/ZnP(As)4 bowl-like shapes we might suppose the existence of “internal” electron delocalization inside the ZnP(P)4/ZnP(As)4 “bowls”. Noticeable reduction of the HOMO/LUMO gaps was calculated for ZnP(P)4 and ZnP(As)4, by ca. 1.10 and 1.47 eV, respectively, compared to ZnP. The core-modification of porphyrins by P and especially by As was found to result in significant decrease of the charge on Zn-centers, by ca. 0.61—0.67e for P and by ca. 0.69—0.76e for As. Charges on P- and As-centers were computed to have large positive values, ca. 0.41—0.45e and ca. 0.43—0.47e, for P and As, respectively, compared to significant negative values, ca. −0.65 to −0.66e for N. The porphyrin core-modification by heavier N congeners, P and As, can noticeably modify the structures, electronic, and optical properties of porphyrins, thus affecting their reactivity and potential applications.

PHYSICS OF THE MIND: OPINION DYNAMICS AND DECISION MAKING PROCESSES BASED ON A BINARY NETWORK MODEL

2008 ◽  
Vol 22 (25n26) ◽  
pp. 4482-4494 ◽  
Author(s):  
F. V. KUSMARTSEV ◽  
KARL E. KÜRTEN
Keyword(s):  
Decision Making ◽  
Social Networks ◽  
Chaotic Behavior ◽  
Opinion Dynamics ◽  
Human Mind ◽  
Critical Parameters ◽  
Opinion Formation ◽  
Natural Catastrophes ◽  
Risk Condition ◽  
Binary Network

We propose a new theory of the human mind. The formation of human mind is considered as a collective process of the mutual interaction of people via exchange of opinions and formation of collective decisions. We investigate the associated dynamical processes of the decision making when people are put in different conditions including risk situations in natural catastrophes when the decision must be made very fast or at national elections. We also investigate conditions at which the fast formation of opinion is arising as a result of open discussions or public vote. Under a risk condition the system is very close to chaos and therefore the opinion formation is related to the order disorder transition. We study dramatic changes which may happen with societies which in physical terms may be considered as phase transitions from ordered to chaotic behavior. Our results are applicable to changes which are arising in various social networks as well as in opinion formation arising as a result of open discussions. One focus of this study is the determination of critical parameters, which influence a formation of stable mind, public opinion and where the society is placed “at the edge of chaos”. We show that social networks have both, the necessary stability and the potential for evolutionary improvements or self-destruction. We also show that the time needed for a discussion to take a proper decision depends crucially on the nature of the interactions between the entities as well as on the topology of the social networks.

scholarly journals The Combination of Pairwise and Group Interactions Promotes Consensus in Opinion Dynamics

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xiaoxuan Liu ◽  
Changwei Huang ◽  
Haihong Li ◽  
Qionglin Dai ◽  
Junzhong Yang
Keyword(s):  
Complex Systems ◽  
Numerical Simulations ◽  
Complete Graph ◽  
Group Interaction ◽  
Opinion Dynamics ◽  
Pairwise Interaction ◽  
Network Structures ◽  
Opinion Formation ◽  
Group Interactions ◽  
Bounded Confidence

In complex systems, agents often interact with others in two distinct types of interactions, pairwise interaction and group interaction. The Deffuant–Weisbuch model adopting pairwise interaction and the Hegselmann–Krause model adopting group interaction are the two most widely studied opinion dynamics. In this study, we propose a novel opinion dynamics by combining pairwise and group interactions for agents and study the effects of the combination on consensus in the population. In the model, we introduce a parameter α to control the weights of the two interactions in the dynamics. Through numerical simulations, we find that there exists an optimal α , which can lead to a highest probability of complete consensus and minimum critical bounded confidence for the formation of consensus. Furthermore, we show the effects of α on opinion formation by presenting the observations for opinion clusters. Moreover, we check the robustness of the results on different network structures and find the promotion of opinion consensus by α not limited to a complete graph.

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