Foreword: Introduction to the Special Issue

Journal of Optimization Theory and Applications -     

Special Issue Dedicated to Professor Paul H.Rabinowitz's 80th Birthday

The conference Calculus of Variations—A celebration of Paul Rabinowitz's 80th birthday was held during Oct.31-Nov.2,2019 at UniHotel Jeju,Korea.The conference was dedi-cated to Professor Paul Rabinowitz on the occasion of his 80th birthday.The current special issues in the journal Analysis in Theory and Applications are formed by papers contributed by speakers in this conference.     

Preface Special Issue Dedicated to Professor Paul H. Rabinowitz’s 80th Birthday

正The conference Calculus of Variations—A celebration of Paul Rabinowitz’s 80th birthday was held during Oct. 31-Nov. 2, 2019 at UniHotel Jeju, Korea. The conference was dedicated to Professor Paul Rabinowitz on the occasion of his 80th birthday.     

The Special Issue Is Dedicated to Prof Li Tatsien on the Occasion of His 70th Birthday

Professor Li has published more than 200 papers and 16 monographs and textbooks, among which 4 monographs are printed in English in U.S.A., U.K. and France respectively. He has received domestic prizes and awards, including: Shanghai Top Science and Technology Award, Hua Loo-Keng Prize of Mathematics, one Second Prize and one Third Prize of National Natural Sciences from the State, one First Prize of Scientific and Technological Progress from the State Education Commission, and one First Prize of Scientific and Technological Progress from Shanghai Municipality. Two of his works are awarded as Excellent University Textbooks from the State. One Exceptional Shanghai Award for Teaching Achievements in Higher Education and one First National Award for Teaching Achievements in Higher Education. Moreover, he has received the Science and Technology Progress Award of Ho Leug Ho Lee Foundation.     

Introduction to the Special Issue

Journal of Optimization Theory and Applications -     

Introduction to the Special Issue

In the model, each person in a large population chooses between two options, such as adhering to or not adhering to a social norm. People observe each others’ choices at random and adjust their adherence probabilities in imitative directions. It is known from earlier work that, under strong restrictions on the imitation, the distribution of adherence probabilities will either evolve upward toward a high adherence equilibrium or downward toward a low adherence equilibrium, depending on initial conditions. The intuition is that imitation leads to uniformity. Here we show that more general forms of imitation allow a much wider variety of outcomes. There can be a sizable number of equilibria and a variety of stability patterns. In mathematical form, the model is an interactive Markov chain.