Guangwang Su

This study investigates a spatiotemporal model for the spread of a viral infection, which incorporates two different types of ages, susceptibility age [ ], and infection age [ ], and spatial heterogeneity of the environment. The investigated model considers a generalized nonlinear incidence function that introduces additional complexity to the disease dynamics. By employing the theory of semigroups, we identify the basic reproduction number [ ], which is characterized as the spectral radius of the next-generation operator. We further identify the sensitivity of this number with respect to the dispersion coefficient [ ]. The principal aim is to investigate the global dynamics governed by [ ], and spotlighting the mathematical challenges obtained by considering both, the nonlinear incidence function, and the susceptible age dependent. Indeed, when [ ], it is obtained that the virus-free steady state is globally asymptotically stable. In contrast, if [ ], the solution map is proven to be uniformly persistent, and the positive steady state becomes globally asymptotically stable. These results are established through the application of Lyapunov functionals applied to the total trajectories system. Additionally, we explore the asymptotic profiles of the positive steady state for large dispersion rates, shedding light on the effect of large diffusion rate of the positive steady state.

In this paper, we introduce the notion of epsilon-contractive maps in fuzzy metric space (X, M, *) and study the periodicities of epsilon-contractive maps. We show that if (X, M, *) is compact and f : X -> X is epsilon-contractive, then P(f) = boolean AND(infinity)(n=1)f(n)(X) and each connected component of X contains at most one periodic point of f, where P(f) is the set of periodic points off. Furthermore, we present two examples to illustrate the applicability of the obtained results.

We consider a type of fuzzy viscoelastic integro‐differential model in this paper. With the aid of some appropriate hypotheses, a unified method and the multiplier technique are implemented to get priori estimates precisely without constructing any auxiliary function. By establishing the estimation of energy function, we derive the stability result of the global solution, and we calculate the estimations of energy attenuation in exponential and polynomial forms, respectively.

In this paper, we present a predator-prey system with mutual interference and distributed time delay and study its dynamical behavior. Based on the existence and universality of mutual interference among species, it is necessary to further study an impulsive food web system. By using stability theory, slight perturbation technique, and comparison theorem, we obtain some theoretical results of the system, such as boundedness and permanence. Moreover, numerical experiments are used to verify the theoretical results and to explore the dynamical behavior of the system, which exhibits rich dynamical behavior such as chaotic oscillation, periodic oscillation, symmetry-breaking bifurcations, chaotic crises, and period bifurcation. Finally, we give some practical guidelines for biological systems based on the theoretical results and numerical experiments of the system.

Let f be a continuous map on a dendrite D with f (D) = D. Denote by R(f ) and AP (f ) the set of recurrent points and the set of almost periodic points of f , respectively, and denote by ω(x, f ), Λ(x, f ), Γ(x, f ) and Ω(x, f ) the set of ω-limit points, the set of α-limit points, the set of γ-limit points and the set of weak ω-limit points of x under f , respectively. In this paper, we show that the following statements are equivalent: (1) D = R(f ). (2) D = AP (f ). (3) Ω(x, f ) = ω(x, f ) for any x ∈ D. (4) Ω(x, f ) = Γ(x, f ) for any x ∈ D. (5) f is equicontinuous. (6) [c, d] ⊄ Ω(x, f ) for any c, d,x ∈ D with c ≠ (7) Ω(x, f ) is minimal for any x ∈ D. (8) Card(Λ ^{− 1}(x, f ) ∩ (D−End(D))) < ∞ for any x ∈ D, where Λ ^{− 1}(x, f ) = {y : x ∈ Λ(y, f )}, End(D) is the set of endpoints of D and Card(A) is the cardinal number of set A. (9) If x ∈ Λ(y, f ) with x, y ∈ D, then y ∈ ω(x, f ). (10) Map h : x → ω(x, f ) (x ∈ D) is continuous and for any x, y ∈ D with x ∉ ω(y, f ), ω(x, f ) ≠ ω(y, f ). Besides, we also study characteristic of pointwise-recurrent maps on a dendrite with the number of branch points being finite.