Browsing by Author "Wu, Chang-Hong"

Now showing 1 - 4 of 4

Absolute stability and synchronization in neural field models with transmission delays
(2016-08-01)
Kao, Chiu-Yen
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Shih, Chih-Wen
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Wu, Chang-Hong
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應用數學系
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Department of Applied Mathematics
Neural fields model macroscopic parts of the cortex which involve several populations of neurons. We consider a class of neural field models which are represented by integro-differential equations with transmission time delays which are space-dependent. The considered domains underlying the systems can be bounded or unbounded. A new approach, called sequential contracting, instead of the conventional Lyapunov functional technique, is employed to investigate the global dynamics of such systems. Sufficient conditions for the absolute stability and synchronization of the systems are established. Several numerical examples are presented to demonstrate the theoretical results. (C) 2016 Elsevier B.V. All rights reserved.
Different spreading speeds in a weak competition model with two free boundaries
(2019-10-05)
Wu, Chang-Hong
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應用數學系
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Department of Applied Mathematics
In this paper, we focus on the spreading behavior of a two-species weak competition system with two free boundaries in a spherically symmetric setting. This model may describe how two weakly competing species spread into the right empty space. When both two species spread successfully and one species cannot keep pace with the other one, it can be expected that two species spread asymptotically in a linear fashion but spread with different speeds. By the help of a semi-wave system and a construction of supersolution and subsolution, we establish the precise spreading speeds and population distribution of two weakly competing species, which provides a new spreading behavior. (C) 2019 Elsevier Inc. All rights reserved.
SEMI-EXACT SOLUTIONS AND PULSATING FRONTS FOR LOTKA-VOLTERRA SYSTEMS OF TWO COMPETING SPECIES IN SPATIALLY PERIODIC HABITATS
(2020-01-01)
Chen, Chiun-Chuan
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Huang, Yin-Liang
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Hung, Li-Chang
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Wu, Chang-Hong
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應用數學系
We are concerned with the coexistence states of the diffusive Lotka-Volterra system of two competing species when the growth rates of the two species depend periodically on the spacial variable. For the one-dimensional problem, we employ the generalized Jacobi elliptic function method to find semi-exact solutions under certain conditions on the parameters. In addition, we use the sine function to construct a pair of upper and lower solutions and obtain a solution of the above-mentioned system. Next, we provide a sufficient condition for the existence of pulsating fronts connecting two semi-trivial states by applying the abstract theory regarding monotone semiflows. Some numerical simulations are also included.
THE SIGN OF TRAVELING WAVE SPEED IN BISTABLE DYNAMICS
(2020-06-01)
Guo, Jong-Shenq
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Nakamura, Ken-Ichi
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Ogiwara, Toshiko
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Wu, Chang-Hong
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應用數學系
We are concerned with the sign of traveling wave speed in bistable dynamics. This question is related to which species wins the competition in multiple species competition models. It is well-known that the wave speed is unique for traveling wave connecting two stable states. In this paper, we first review some known results on the sign of wave speed in bistable two species competition models. Then we derive rigorously the sign of bistable wave speed for a special three species competition model describing the competition in two different circumstances: (1) two species are weak competitors and one species is a strong competitor; (2) three species are very strong competitors. It is interesting to observe that, under certain conditions on the parameters, two weaker competitors can wipe out the strongest competitor.