Lecture Room B, 4th Floor, The 3rd General Building, NTHU

**Speaker:**

Xing Liang (University of Science and Technology of China)

Te-Sheng Lin (National Chiao Tung University)

Stephen Alexander Gourley (University of Surrey)

Feng-Bin Wang (Chang Gung University)

**Organizers:**

Sze-Bi Hsu (National Tsing Hua University)

Je-Chiang Tsai (National Taiwan Normal University)

Feng-Bin Wang (Chang Gung University)

**Goal**

It is believed that the understanding of the dynamics in biological systems plays a key role in extracting biological mechanisms. Motivated by this, we will introduce some mathematical tools to analyze the dynamical behavior observed in a number of biological models, and then give the biological implications of these studies. The following topics will be covered.

(1) Dynamics and propagation phenomena of reaction-diffusion equations;

(2) Applications of delay equations;

(3) Mathematical models with resource storage

(4) Bifurcation analysis of evolutional equations.

**Speaker**

(i) Professor Xing Liang

School of Mathematics Sciences, University of Science and Technology of China, China Title: Dynamics and propagation phenomena of reaction-diffusion equations

Abstract:

In this lecture, we will consider the reaction-diffusion equation ut = A[u] + f(x, t, u). Here A is supposed to be a second-order uniformly elliptic operator. We always suppose that the domain under considearation is a domain in the n-dimensional Euclidean space or the entire Euclidean space.

(ii) Professor Stephen Alexander Gourley

Department of Mathematics, University of Surrey, Guildford, Surrey, UK

Title: Applications of delay equations

Lecture 1: Introduction to the applications of delay equations.

Abstract: I will illustrate the wide range of applications of delay differential equations, including both engineering and biological applications, with an emphasis on what we can learn from linearised analysis.

Lecture 2: Delay equations in the study of insect-borne diseases.

Abstract: Insect-borne diseases include diseases that are carried by flying insects, such as malaria (carried by mosquitoes) and bluetongue (carried by midges). This talk will include an overview of some delay equation models for insect-borne diseases. More sophisticated models can incorporate insecticiding and the problem of insecticide resistance.

Lecture 3: Age-dependent toxicity in plant chemical defences and herbivore feeding behaviour.

Abstract: This lecture will show how we can use age-dependence and delay equations to aid our understanding of the evolution of plant chemical defenses and herbivore feeding behaviour.

(iii) Professor Feng-Bin Wang

Division of Natural Science, Center for General Education, Chang Gung University

Title: Modeling the earthquake in the southwestern region of Taiwan using a biological delay equation

*** **This is an open discussion on modeling the earthquake in the southwestern region of Taiwan.

Kuo-Sen Huang (NCREE) will first give an introduction on this topic, and Prof. Feng-Bin Wang will be the chairman in the subsequent discussion.

(iv) Professor Te-Sheng Lin

Department of Applied Mathematics, National Chiao Tung University

Title: Bifurcation analysis of evolution equations with the help of scientific computation Abstract:

In this lecture, we will cover the following topics.

1.Numerical time simulation of general evolution equations.

2.Numerical continuation with ATUO07p.

3.Bifurcation analysis of evolution equation using AUTO07p and FFTW.

**Program**

(i) Professor Xing Liang

1.Some qualitative properties of linear heat equations and KPP equations

Time: 10:00-12:00,14:00-16:00, August 3, 2017

2. Some qualitative properties of bistable equations and dynamics of the system of reaction-diffusion equations with comparison principle

Time: 10:00-12:00,14:00-16:00, August 4, 2017

(ii) Professor Stephen Alexander Gourley

1.Introduction to the applications of delay equations.

Time: 10:00-12:00, August 7, 2017

2. Delay equations in the study of insect-borne diseases.

Time: 10:00-12:00, August 8, 2017

3.Age-dependent toxicity in plant chemical defences and herbivore feeding behaviour

Time: 10:00-12:00, August 9, 2017

(iii)Professor Feng-Bin Wang

1. Modeling the earthquake in the southwestern region of Taiwan using a biological delay equation

Time: 14:00-16:00, August 7, 2017

2. Modeling the earthquake in the southwestern region of Taiwan using a biological delay equation

Time: 14:00-16:00, August 8, 2017

3. Modeling the earthquake in the southwestern region of Taiwan using a biological delay equation

Time: 14:00-16:00, August 9, 2017

(iv) Professor Te-Sheng Lin

1.Numerical time simulation of general evolution equations

Time: 10:00-12:00,14:00-16:00, August 14, 2017

2.Numerical continuation with ATUO07p

Time: 10:00-12:00,14:00-16:00, August 15, 2017

3.Bifurcation analysis of evolution equation using AUTO07p and FFTW

Time: 10:00-12:00,14:00-16:00, August 16, 2017

__**The course will include lectures and tutorials**__

**Contact:**
Vicky, 03-574-5254, sunug@math.cts.nthu.edu.tw

Poster: events_3_98170602322985116.jpg