A model of cumulative advantage for conference dynamics

Abstract

This paper attempts to modify the standard Verhulst model to describe the dynamics of scientific conferences taking into account cumulative advantage.

Full Text

1.     Introduction

The problem of conference evaluation is currently very pressing for researchers in the field of scientometrics, as there is no universal methodology for evaluating all conferences in all fields. Several conference rankings exist, such as the Australian CORE, the Chinese CCF Conference Rankings, the Brazilian QUALIS, and the industry-specific Microsoft Academic Conference Rankings. All of these rankings are compiled for computer science conferences, due to the extremely important nature of conferences in this field, as over 60% of research results are published in conference proceedings.

A study of the development of scientific conferences showed that conferences develop unevenly, with some becoming stellar, while others quickly fade away. This led us to use the standard Verhulst

model [1] for our study, but to expand it by taking into account the Matthew effect [2].

2.     Basic model

Let there be 𝑛 conferences in a given scientific field. Let 𝑅^𝑖(𝑡) ⩾ 0 denote the numerical measure of the ranking of the 𝑖th conference at time 𝑡. The ranking is considered as a single aggregate value. Let the ranking dynamics of each conference be determined by the following mechanisms:

• internalgrowth;
• competition;
• naturaldecay; – external influences.

© 2026 Ermolayeva, A. M.

                               This work is licensed under a Creative Commons “Attribution-NonCommercial 4.0 International” license.

                                                                               Letters                                                               ACS. 2026, 34 (1), 145–149

Internal growth is associated with the desire to increase ratings through internal efforts (attracting renowned speakers, improving the quality of peer review, and improving organization). Competition is caused by the mutual inhibition of conferences, as resources (people, money) are limited. Natural decay (dissipation) is associated with obsolescence, loss of relevance, etc. External influences are caused by unpredictable factors (black swans) (e.g., changes in program committees, publication of breakthrough results, scandals).

We will use the Verhulst model for an isolated conference as a basis:

                                                                𝑑𝑅                         𝑅

                                                                 = 𝑟𝑅 (1 −    ) − 𝛿𝑅,

                                                                 𝑑𝑡                         𝐾

where 𝑟 is the maximum growth rate, 𝐾 is the capacity (the maximum achievable rating in the absence of competitors), 𝛿 is the decay coefficient.

Then the equilibrium rating is:

                                                              𝑅^∗ = 𝐾(1 − 𝛿/𝑟),              𝑟 > 𝛿.

We’ll introduce competitive inhibition for several conferences. The growth of each conference is slowed not only by its own rankings, but also by the rankings of other conferences.

∑𝑛𝑗=1 𝛼𝑖𝑗𝑅𝑗

                                                           𝑑𝑅𝑖                𝑖 (1 −                            ),

= 𝑟𝑖𝑅

                                                            𝑑𝑡                                       𝐾_𝑖

where 𝛼_𝑖𝑗 is the coefficient of influence of conference 𝑗 on conference 𝑖. It is natural to assume 𝛼_𝑖𝑖 = 1.

𝛼_𝑖𝑗 for 𝑖 ≠ 𝑗 shows how strongly competitors suppress the growth of the 𝑖th conference.

Let’s add attenuation and external influences:

𝑑𝑅𝑖 𝑖 (1 − ∑𝑛𝑗=1 𝛼𝑖𝑗𝑅𝑗 ) − 𝛿𝑖𝑅𝑖 + 𝛾𝑖𝐹𝑖(𝑡), = 𝑟𝑖𝑅

                                               𝑑𝑡                                       𝐾_𝑖

where:

• 𝑟_𝑖 > 0 — potential growth rate,
• 𝐾_𝑖 > 0 — maximum possible rating in the absence of competitors,
• 𝛼_𝑖𝑗 ⩾ 0 — competition coefficients,
• 𝛿_𝑖 ⩾ 0 — natural decay rate,
• 𝛾_𝑖 ⩾ 0 — sensitivity to external influences, – 𝐹_𝑖(𝑡) ⩾ 0 — external impulse function.

In a more compact form, we can rewrite:

                                                 𝑑𝑅𝑖                  𝑖 (𝑟𝑖 − 𝑟𝑖 ∑𝑛 𝛼𝑖𝑗𝑅𝑗 − 𝛿𝑖) + 𝛾𝑖𝐹𝑖(𝑡).

= 𝑅

                                                  𝑑𝑡                            𝐾𝑖 _𝑗=1

The term − ^𝑟𝑖 𝛼_𝑖𝑗𝑅^𝑖𝑅^𝑗 describes mutual inhibition.

𝐾_𝑖

3.     Accounting for Matthew’s law

Matthew’s Law (for to everyone who has, more will be given, and he will have abundance; but from him who does not have, even what he has will be taken away) is a manifestation of cumulative advantage. The higher a conference’s rating, the easier it is to attract the best authors, receive more citations, and, consequently, further increase its rating.

Ermolayeva,A.M. A model of cumulative advantage for conference dynamics                                                                                               147

3.1.      Dependence on the current rating

Let’s add the term 𝛽_𝑖𝑅^𝑖_𝜃, which increases the growth rate proportionally to the current rating:

𝑑𝑅𝑑𝑡𝑖 = 𝑟𝑖𝑅𝑖 (1 − ∑𝛼𝐾𝑖𝑗𝑖 𝑅𝑗 ) + 𝛽𝑖𝑅𝑖𝜃 − 𝛿𝑖𝑅𝑖 + 𝛾𝑖𝐹𝑖(𝑡),

where:

– 𝛽_𝑖 ⩾ 0 — intensity of the cumulative advantage, – 𝜃 > 0 — nonlinearity index.

3.2.      Capacity dependence on rating

Let’s make the capacity 𝐾_𝑖 dependent on the rating:

𝐾𝑖 = 𝐾𝑖(0) + 𝜘𝑖𝑅𝑖,

where 𝜘_𝑖 ⩾ 0.

Then the logistical constraint becomes less severe for the leaders, which facilitates their further growth.

3.3.      Asymmetric competition

To take Matthew’s law into account, we can make 𝛼_𝑖𝑗 dependent on the difference in ratings:

                                                  𝛼𝑖𝑗 = 𝛼𝑖𝑗base ⋅ exp(−𝜆(𝑅𝑖 − 𝑅𝑗)),                 𝑅𝑖 > 𝑅𝑗,

where 𝜆 > 0.

A conference with a higher rating 𝑅^𝑖 experiences less inhibition from a conference with a lower 𝑅^𝑗. This creates a positive feedback loop: leaders become less vulnerable to competitors.

3.4.     Threshold effect

If the cumulative advantage is very strong, the system may exhibit bistability. The conference either becomes a leader or remains at a low level. To achieve this, we add a threshold term:

                                                      ^𝑑𝑅𝑑𝑡^{𝑖                   𝑖} (𝜌_𝑖(𝑅^𝑖 − 𝑅th)) − 𝛿_𝑖𝑅^𝑖 + …

= 𝑅

3.5.      Cumulative advantage

Cumulative advantage means that the rating increase is proportional to the current rating (or its degree) with a positive coefficient. In the simplest case (𝛽_𝑖 > 0, 𝜃 = 1) at the initial stage we obtain:

                                                                     𝑑𝑅𝑖                             𝑖.

≈ (𝑟𝑖 + 𝛽𝑖)𝑅

𝑑𝑡

This leads to exponential growth, limited only by the capacity 𝐾_𝑖 and competition. If two conferences initially have similar parameters, but one gains a small advantage 𝜀, this advantage will increase over time, and the system may converge to an equilibrium with a strong leader dominance.

The equilibrium becomes unstable, and a “winner-takes-all” regime emerges.