On a Multi-Delay Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion

Wang, Changyou; Li, Nan; Zhou, Yuqian; Pu, Xiaorong; Li, Rui

doi:10.1007/s10473-019-0209-3

Cited by 7 publications

(4 citation statements)

References 37 publications

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“…However, the convexity analysis shows 0 < α < 1 is just a sufficient condition of blowup, which implies cannot be directly applied to treat the case of α > 1. Indeed, a standard calculation shows its second order derivative J ′′ ( t ) in time has not definite sign, even for the system with negative energy . In this paper, we eventually introduce a new modification

F (t) = ‖ ψ ‖_{L^{2}}^{2} + {‖D^{- 1} (ϕ - {scriptT}_{N} ϕ_{0})‖}_{L^{2}}^{2},

where

T_{N} ϕ_{0}

is a truncation of the initial data ϕ 0 and obtain the following blow‐up theorem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Klein‐Gordon‐Zakharov system in energy space: Blow‐up profile and subsonic limit

Shi

Wang

2019

Math Methods in App Sciences

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In this paper, we prove finite‐time blowup in energy space for the three‐dimensional Klein‐Gordon‐Zakharov (KGZ) system by modified concavity method. We obtain the blow‐up rates of solutions in local and global space, respectively. In addition, by using the energy convergence, we study the subsonic limit of the Cauchy problem for KGZ system and prove that any finite energy solution converges to the corresponding solution of Klein‐Gordon equation in energy space.

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F (t) = ‖ ψ ‖_{L^{2}}^{2} + {‖D^{- 1} (ϕ - {scriptT}_{N} ϕ_{0})‖}_{L^{2}}^{2},

where

T_{N} ϕ_{0}

is a truncation of the initial data ϕ 0 and obtain the following blow‐up theorem.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, a standard calculation shows its second order derivative J ′′ (t) in time has not definite sign, even for the system with negative energy. 15,16 In this paper, we eventually introduce a new modification…”

Section: Introductionmentioning

confidence: 99%

Klein‐Gordon‐Zakharov system in energy space: Blow‐up profile and subsonic limit

Shi

Wang

2019

Math Methods in App Sciences

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“…For three-dimensional competition models, the studies of the aforementioned problems become more challenging due to the higher phase space dimension which has attracted much attention from scientist community. Among them, we refer the reader to some references for showing the permanence, [22][23][24][25] extinction, 26,27 existence, [27][28][29][30][31] coexistence, 32 global topological classification, 33 and more references therein.…”

Section: Introductionmentioning

confidence: 99%

Speed determinacy of the traveling waves for a three species time‐periodic Lotka–Volterra competition system

Pan

Wang

2022

Math Methods in App Sciences

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Some physical environmental conditions changing in time create a great difficulty in studying time-periodic traveling wave solutions. In this paper, we investigate speed selection of time-periodic traveling waves for a three species time-periodic Lotka-Volterra competition system. By transforming the competitive system into a cooperative system, the existence of the traveling wave solutions and speed determinacy of the spread speed are studied via the upper-lower solution method as well as the comparison principle. Through constructing specific types of upper and lower solutions to the system, some sets of sufficient conditions composed of the parameters in the system are established to justify the linear and nonlinear selection of the spread speed. As the positive periodic functions in system reduces to the constant coefficients, parts of our results could cover the previous works, and the other results are novel.

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“…Notably, the Lotka-Volterra models were proposed by Lotka [2] and Volterra [3] for the first time, and now they have become the most important means to explain this type of ecological phenomenon. In particular, the Lotka-Volterra competitive model, mutualism (cooperative) model, and predator-prey model characterize competitive, cooperative, and predator-prey interactions between species that are of great interest in the study of dynamical behaviors of systems [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. However, pure competition as described by the Lotka-Volterra model often results in species exclusion or coexistence with reduced carrying capacity of both species and does not help the coexistence of multiple species, although it is a driving force for natural selection [1].…”

Section: Introductionmentioning

confidence: 99%

Dynamics in a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays

Muhammadhaji

Halik

2021

Adv Differ Equ

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This study investigates the dynamical behavior of a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays. Compared with previous studies, both ratio-dependent functional responses and time delays are considered. By employing the comparison method, the Lyapunov function method, and useful inequality techniques, some sufficient conditions on the permanence, periodic solution, and global attractivity for the considered system are derived. Finally, a numerical example is also presented to validate the practicability and feasibility of our proposed results.

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On a Multi-Delay Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion

Cited by 7 publications

References 37 publications

Klein‐Gordon‐Zakharov system in energy space: Blow‐up profile and subsonic limit

Klein‐Gordon‐Zakharov system in energy space: Blow‐up profile and subsonic limit

Speed determinacy of the traveling waves for a three species time‐periodic Lotka–Volterra competition system

Dynamics in a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays

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