Incorporating two delays (τ 1 represents the maturity of predator, τ 2 represents the maturity of top predator), we establish a novel delayed three-species food-chain model with stage structure in this paper. By analyzing the characteristic equations, constructing a suitable Lyapunov functional, using Lyapunov-LaSalle's principle, the comparison theorem and iterative technique, we investigate the existence of nonnegative equilibria and their stability. Some interesting findings show that the delays have great impacts on dynamical behaviors for the system: on one hand, if τ 1 ∈ (m 1 , m 2 ) and τ 2 ∈ (m 4 , +∞), then the boundary equilibrium E 2 (x 0 , y 0 1 , y 0 2 , 0, 0) is asymptotically stable (AS), i.e., the prey species and the predator species will coexist, the top-predator species will go extinct; on the other hand, if τ 1 ∈ (m 2 , +∞), then the axial equilibrium E 1 (k, 0, 0, 0, 0) is AS, i.e., all predators will go extinct. Numerical simulations are great well agreement with the theoretical results.

No abstract

Incorporating blockchain technology, this paper focuses on solving inventory financing difficulties of small and medium-sized enterprises(SMEs). Different from the existing financing model, we provide a new way for SMEs to obtain loan finacing services without the involvement of core companies. Related concepts and main charateristics of blockchain are introduced. Data flow model of new inventory financing and its design details about how to apply these blockchain technology are described. Finally, we present its innovative advantages in solving the financing difficulties of SMEs.

By taking full consideration of maturity (τ 1 represents the maturity of predator and τ 2 represents the maturity of top predator) and the effects of environmental parameters, a new delayed three-species food chain model with stage structure and time-varying coefficients is established. With the help of the comparison theorem and the technique of mathematical analysis, the positivity and boundedness of solutions of the model are investigated. Furthermore, some sufficient conditions on the permanence and partial extinction of the system are derived. Some interesting findings show that the delays have great impacts on the permanence for the system. More precisely, if τ 2 ∈ (n, +∞), then the system is partially extinct: on one hand, if τ 1 ∈ (0, n 1 ) and τ 2 ∈ (n, +∞), then the prey and predator species will coexist, i.e., both the prey and predator species are always permanent, yet the top predator species will go extinct eventually. On the other hand, if τ 1 ∈ (n 4 , +∞) and τ 2 ∈ (n, +∞), where n 4 is greater than n 1 , then all predator species will become extinct eventually. Numerical simulations are great well agreement with the theoretical results.