References
- Wang Q , Gai C , Yan J . Qualitative analysis of a Lotka--Volterra competition system with advection. Discrete Contin Dyn Syst. 2015;35(3):1239–1284.
- Wang Q , Zhang L . On the multi-dimensional advective Lotka-Volterra competition systems. Nonlinear Anal Real World Appl. 2017;37:329–349.
- Shi J . Absolute stability and conditional stability in general delayed differential. In: Advances in interdisciplinary mathematical research, Springer proceedings in mathematics & statistics, Vol. 37. New York (NY): Springer; 2013. p. 117–131.
- Kato T . Functional analysis. Springer classics in mathematics; 1995.
- Amann H . Hopf bifurcation in quasilinear reaction-diffusion systems. In: Delay differential equations and dynamical systems. Vol. 4, Lecture notes in mathematics. Berlin: Springer; 1991. p. 1475.
- Crandall MG , Rabinowitz PH . The hopf bifurcation theorem in infinite dimensions. Arch Rat Mech Anal. 1977;67:53–72.
- Conway E , Hoff D , Smoller J . Large time behavior of solutions of systems of nonlinear reaction-diffusion equations. SIAM J Appl Math. 1978;35:1–16.
- De Mottoni P , Rothe F . Convergence to homogeneous equilibrium state for generalized Volterra-Lotka systems with diffusion. SIAM J Appl Math. 1979;37:648–663.
- Kishimoto K , Weinberger H . The spatial homogeneity of stable equilibria of some reaction-diffusion systems in convex domains. J Differ Equ. 1985;58:15–21.
- Mimura M , Ei S-I , Fang Q . Effect of domain-shape on coexistence problems in a competition-diffusion system. J Math Biol. 1991;29:219–237.
- Wang Q , Zhang L , Yang J , et al . Global existence and steady states of a two competing species Keller-Segel chemotaxis model. Kinet Relat Models. 2015;8:777–807.
- Wang Q , Yang J , Zhang L . Time-periodic and stable patterns of a two-competing-species Keller-Segel chemotaxis model: effect of cellular growth. Discrete Contin Dyn Syst Ser B. 2017;22(9):3547–3574.
- Chen S , Shi J , Wei J . Time delay-induced instabilities and Hopf bifurcations in general reaction-diffusion systems. J Nonlinear Sci. 2013;23:1–38.
- Li X , Wei J . On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays. Chaos Solitons Fractals. 2005;26:519–526.