Cui-Ping Cheng’s research while affiliated with University of Shanghai for Science and Technology and other places

... Based on the effects of viscous dissipation and Joule heating, Feng et al. 36 analyzed the electro-osmotic flow and heat transfer of a Maxwell fluid with distributed order time fractional characteristics in a microparallel channel under the action of an alternating field. Duan et al. 40 discussed and compared, in detail, the single-degree-of-freedom steady-state vibrations of a single fractional derivative and distributed derivative under a harmonic drive. Qiao et al. 41 studied the influence of distributed/varied order time fractional Maxwell constitutive models on viscoelastic fluid flows driven by periodic pressure gradients in an infinite straight pipe, derived numerical solutions, and verified their accuracy and applicability. ...

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Electro-osmotic flow of generalized Maxwell fluids in triangular microchannels based on distributed order time fractional constitutive model

... Lattice systems can be viewed as spatial discretizations of PDEs, which have many applications in pattern formation, chemical reaction, propagation of nerve pulses, and electric circuits, see [5,14,19,25,27] and the references therein for more details and examples. The mathematical topics on lattice systems have attracted more and more attentions in the literature, such as traveling wave solutions, chaotic solutions, attractors, and invariant measures, see, e.g., [12]. In particular, pathwise random attractors of stochastic lattice systems/PDEs driven by linear multiplicative noise or additive noise were investigated in [3, 4, 8-10, 13, 20-24, 34, 40, 47, 48, 50-54]. ...

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Random Attractor, Invariant Measures, and Ergodicity of Lattice p-Laplacian Equations Driven by Superlinear Noise

... Lattice differential equations are the discrete versions of reaction-diffusion equations. In past few years, many authors have paid their attention on the existence of traveling wave solutions for lattice differential equations, see [3,4,7,8,13,16,17,21] for one or two dimensional lattices and [15,20,22] for higher dimensional lattices, and also see the results for reaction-diffusion equations with or without stage structure [1,2,5,6,9,10,14,18,19]. ...

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Traveling wave solutions in a higher dimensional lattice competition-cooperation system with stage structure

... Dispersal evolution is better understood in the context of stable range margins, where habitat isolation and spatial heterogeneity in patch quality can result in low dispersal rates (Bonte et al. 2010;Kubisch et al. 2014). In general, low dispersal ability in stable range populations has a selective advantage when habitat quality is variable over space (Hastings 1983;Holt 1985;Roff 1990;Denno et al. 2001;Hutson et al. 2001;Kao et al. 2010;Wang et al. 2016). Based on these results, spatial sorting may not be a dominant process during range expansions through patchy environments. ...

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Trait correlations and landscape fragmentation jointly alter expansion speed via evolution at the leading edge in simulated range expansions

... where r i , a i , b i > 0, i = 1, 2, τ j > 0, j = 1, 2, 3, 4. Now we recall some conclusions about the traveling waves of different dimensional lattice equations with or without delays. In past few years, great progress has been made in the traveling wave solutions for a single equation, see [1], [2], [3], [4], [5], [6], [8], [10], [11], [16], [17], [18], [25], [20], [21], [22], [24], [26], [27], [29] for 1 or 2 dimensional lattices and [19], [23], [28] for higher dimensional lattices. Recently, many authors also paid their attention to the traveling waves for systems with two equations. ...

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Traveling wave solutions in a class of higher dimensional lattice differential systems with delays and applications

... The dispersal coefficients p i,j , q i,j > 0 and satisfy p i+N1,j = p i,j = p i,j+N2 , q i+N1,j = q i,j = q i,j+N2 , the reaction function satisfies f i,j (·) = f i+N1,j (·) = f i,j+N2 (·) for all i, j ∈ Z. In [2], Cheng et al. established the existence, stability and uniqueness of pulsating (or periodic) traveling fronts (see Definition 1.1) of system (2) with monostable nonlinearity. Wu [31] studied the existence and uniqueness of pulsating (or periodic) traveling fronts of system (2) with homogeneous and bistable nonlinearity. ...

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Entire solutions in a two-dimensional nonlocal lattice dynamical system

... In the past decades, there are a lot of works devoted to the existence, asymptotic behavior, uniqueness and stability of traveling waves for lattice dynamical systems in spatially periodic or homogeneous media, one can refer to [1,7,8,9,14,2,3,4,5,6,16,18,29,17,20]. For spatially periodic environment, the pulsating traveling front is a key object in characterizing the dynamics of lattice differential equations, such as (1), but it is not enough to understand the whole dynamics. ...

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Entire solutions in a two-dimensional nonlocal lattice dynamical system

... The existence of traveling wave solutions for the bistable system (1) has been considered in [5], see also [6] for general results on the existence of bistable traveling waves. In the current study, we focus on the monotonicity problem of traveling waves, we shall prove that any wave profile is strictly increasing. ...

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Monotonicity of wave profiles for a bistable system on 2-D lattice

... These can be seen in [9,14,29,37] and the references therein. Recently, there is a particular interest on studying the species population living in a patchy environment consisting of all integer nodes, see [7,8,34,35]. ...

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Global stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction

... By analyzing the location of the spectrum, the local stability of the traveling waves are investigated [17,18]. For more related works, we refer to [19][20][21][22][23][24][25][26][27][28][29][30][31][32], and the references cited therein. ...

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Global stability of traveling waves in monostable stream-population model