A Dynamical System Approach in Modeling Technology Transfer

Abstract

Abstract. In this paper we discuss a mathematical model of two parties technology transfer from a leader to a follower. The model is reconstructed via dynamical system approach from a known standard Raz and Assa model and we found some important conclusion which have not been discussed in the original model. The model assumes that in the absence of technology transfer from a leader to a follower, both the leader and the follower have a capability to grow independently with a known upper limit of the development. We obtain a rich mathematical structure of the steady state solution of the model. We discuss a special situation in which the upper limit of the technological development of the follower is higher than that of the leader, but the leader has started earlier than the follower in implementing the technology. In this case we show a paradox stating that the follower is unable to reach its original upper limit of the technological development could appear whenever the transfer rate is sufficiently high. We propose a new 'paradox-free' model to increase realism so that any technological transfer rate could only has a positive effect in accelerating the rate of growth of the follower in reaching its original upper limit of the development.Key words and Phrases: Dynamical system, technology transfer, knowledge management, logistic curve. Abstrak. Di dalam makalah ini dibahas sebuah model matematika mengenai transfer teknologi dari seorang individu atau suatu parti yang disebut leader kepada seorang individu atau suatu parti yang disebut follower. Model tersebut direkonstruksi melalui pendekatan sistem dinamik dari model standar Raz-Assa yang sudah dikenal. Hasil analisis model memperlihatkan sebuah sifat dari model hasil rekonstruksi yang tidak ada dalam bahasan model aslinya. Model Raz-Assa mengasumsikan bahwa ketika tidak ada transfer teknologi, masing-masing individu atau parti mempunyai kapasitas untuk berkembang secara independen menuju batas atas yang diketahui. Selain itu juga diperlihatkan sifat-sifat solusi setimbang dari model tersebut di atas. Kemudian juga dibahas situasi khusus di mana follower mempunyai batas atas perkembangan yang lebih tinggi dibandingkan dengan leader, namun terlambat dalam implementasi teknologi terkait dibandingkan dengan leader tersebut. Dalam situasi seperti ini akan diperlihatkan suatu paradox di mana follower tidak akan pernah mencapai batas atas kapasitasnya apabila laju transfer teknologi terlalu tinggi. Untuk mengatasi paradox ini sebuah model baru diperkenalkan, sehingga laju transfer teknologi selalu memberikan efek positif terhadap follower dalam hal pencapaian batas atas pengembangan teknologinya.

Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

“…In addition to the mentioned issues, several other ecological factors deserve consideration in developing realistic models. These factors include (i) source and sink subpopulation [7,8], (ii) different levels of intraspecific competition [57,58], and (iii) coupled growth function [59]. These elements play a critical role in determining optimal harvesting strategies and the choice between MSY or Quasi MSY as harvesting strategies, as shown in [60].…”

Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level

“…The results above are deduced from the specific assumptions used in the construction of the model. It would be interesting to explore the robustness of the results for other ecological issues that are worthy to be taken into account in developing a more realistic model, such as different levels of intraspecific competition [28], the Allee effect [29,30], fear effect [31,32], and a coupled growth function caused by a metapopulation structure [33], which may alter the result in this study. These are being investigated by the authors.…”

A review on eigen values of adjacency matrix of graph with cliques

“…It is also often some interesting mathematical structures appear in such problems [12,13]. The example of the appearence of eigen value in industrial engineering can be found in [14,15]. Other examples of applications are abound, such as in spectral clustering analysis [16], singular value decomposition for image compression [17], incremental principal component analysis [18], the Google Page Rank algorithm [19].…”