DCDS-B
Allee effect and a catastrophe model of population dynamics
Dianmo Li Zhen Zhang Zufei Ma Baoyu Xie Rui Wang
Discrete & Continuous Dynamical Systems - B 2004, 4(3): 629-634 doi: 10.3934/dcdsb.2004.4.629
Some assumptions of Logistic Equation are frequently violated. We applied the Allee effect to the Logistic Equation so as to avoid these unrealistic assumptions. Following basic principles of Catastrophe theory, this new model is identical to a Fold catastrophe type model. An ecological interpretation of the results is provided.
keywords: catastrophe theory Logistic Equation. Allee effect
DCDS-B
Pullback attractors of FitzHugh-Nagumo system on the time-varying domains
Zhen Zhang Jianhua Huang Xueke Pu
Discrete & Continuous Dynamical Systems - B 2017, 22(10): 3691-3706 doi: 10.3934/dcdsb.2017150

The existence and uniqueness of solutions satisfying energy equality is proved for non-autonomous FitzHugh-Nagumo system on a special time-varying domain which is a (possibly non-smooth) domain expanding with time. By constructing a suitable penalty function for the two cases respectively, we establish the existence of a pullback attractor for non-autonomous FitzHugh-Nagumo system on a special time-varying domain.

keywords: Pullback attractor FitzHugh-Nagumo equation time-varying domain penalty function

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