Nonlinear Analysis: Modelling and Control

Journal Information
ISSN / EISSN : 13925113 / 13925113
Current Publisher: Vilnius University Press (10.15388)
Total articles ≅ 297
Current Coverage
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Latest articles in this journal

Jin-Jin Mao, Shou-Fu Tian, Tian-Tian Zhang, Xing-Jie Yan
Nonlinear Analysis: Modelling and Control, Volume 25, pp 358–377-358–377; doi:10.15388/namc.2020.25.16653

In this work, we consider the chiral nonlinear Schrödinger equation in (2 + 1)-dimensions, which describes the envelope of amplitude in many physical media. We employ the Lie symmetry analysis method to study the vector field and the optimal system of the equation. The similarity reductions are analyzed by considering the optimal system. Furthermore, we find the power series solution of the equation with convergence analysis. Based on a new conservation law, we construct the conservation laws of the equation by using the resulting symmetries.
Sergey Smirnov
Nonlinear Analysis: Modelling and Control, Volume 25, pp 502–508-502–508; doi:10.15388/namc.2020.25.16776

We give a simple geometrical criterion for the nonexistence of constant-sign solutions for a certain type of third-order two-point boundary value problem in terms of the behavior of nonlinearity in the equation. We also provide examples to illustrate the applicability of our results.
Ankit Kumar, Balram Dubey
Nonlinear Analysis: Modelling and Control, Volume 25, pp 417–442-417–442; doi:10.15388/namc.2020.25.16663

This study proposes two prey–predator models with strong and weak Allee effects in prey population with Crowley–Martin functional response. Further, gestation delay of the predator population is introduced in both the models. We discussed the boundedness, local stability and Hopf-bifurcation of both nondelayed and delayed systems. The stability and direction of Hopfbifurcation is also analyzed by using Normal form theory and Center manifold theory. It is shown that species in the model with strong Allee effect become extinct beyond a threshold value of Allee parameter at low density of prey population, whereas species never become extinct in weak Allee effect if they are initially present. It is also shown that gestation delay is unable to avoiding the status of extinction. Lastly, numerical simulation is conducted to verify the theoretical findings.
Andrius Čiginas
Nonlinear Analysis: Modelling and Control, Volume 25, pp 341–357-341–357; doi:10.15388/namc.2020.25.16773

Small area estimation techniques are used in sample surveys, where direct estimates for small domains are not reliable due to small sample sizes in the domains. We estimate the domain means by generalized linear compositions of the weighted sample means and the synthetic estimators that are obtained from the regression-synthetic model of fixed effects, based on the domain level auxiliary information. In the proposed method, the number of parameters of optimal compositions is reduced to a single unknown parameter, which is further evaluated by minimizing an empirical risk function. We apply various composite and related estimators to estimate proportions of the unemployed in a simulation study, based on the Lithuanian Labor Force Survey data. Conclusions on advantages and disadvantages of the proposed compositions are obtained from this empirical comparison.
Jonas Sprindys, Jonas Šiaulys
Nonlinear Analysis: Modelling and Control, Volume 25, pp 509–522-509–522; doi:10.15388/namc.2020.25.16661

Let {ξ1,ξ2,...} be a sequence of independent real-valued, possibly nonidentically distributed, random variables, and let η be a nonnegative, nondegenerate at 0, and integer-valued random variable, which is independent of {ξ1,ξ2,...}. We consider conditions for {ξ1,ξ2,...} and η under which the distributions of the randomly stopped minimum, maximum, and sum are regularly varying.
Parasuraman Loganathan, Krishnamurthy Deepa
Nonlinear Analysis: Modelling and Control, Volume 25, pp 443–460-443–460; doi:10.15388/namc.2020.25.16659

Simulation of electro-magneto-hydrodynamic Casson fluid flow subject to cross stratification and variable chemical reaction is exemplified numerically. The model, which is governed by the system of partial differential equations, accomplishes the implicit finite difference solution. The variable chemical reaction enables the study to investigate an exponentially varying reaction rate along the stratified flow. Further, the mesh-contour plots impart the precise visualization of flow field in 3D and its projection as contour on XY -plane. The stronger chemical reaction parameter improves the temperature and mass transfer rate. The consistency of the results is affirmed by the correlation with results arising in the literature.
Xuejun Yi, Ling Ren, Zhengqiu Zhang
Nonlinear Analysis: Modelling and Control, Volume 25, pp 378–399-378–399; doi:10.15388/namc.2020.25.16656

In this paper, we are concerned with global asymptotic synchronization of Duffing-type oscillator system. Without using matrix measure theory, graph theory and LMI method, which are recently widely applied to investigating global exponential/asymptotic synchronization for dynamical systems and complex networks, four novel sufficient conditions on global asymptotic synchronization for above system are acquired on the basis of constant variation method, integral factor method and integral inequality skills.
Aleksandra Gawlik, Vsevolod Vladimirov, Sergii Skurativskyi
Nonlinear Analysis: Modelling and Control, Volume 25, pp 482–501-482–501; doi:10.15388/namc.2020.25.16842

We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh–Nagumo system describing the nerve impulse propagation in axon. The modeling system is shown to possesses soliton-like solutions under certain restrictions on the parameters. The results of theoretical studies are backed by the direct numerical simulation.
Kanisha Pujaru, T.K. Kar
Nonlinear Analysis: Modelling and Control, Volume 25, pp 400–416-400–416; doi:10.15388/namc.2020.25.16657

This paper gives a broad outline of some comparative analysis of two ecological services, namely, yield and resilience of a generalist predator–prey system. Although either prey or predator species can be harvested at maximum sustainable yield (MSY) level, yet there is a trade-off between yield and resilience. When both the species are harvested simultaneously, MSY increase by changing catchabilities always increases the system resilience both in prey- and predator-oriented fishery. In particular, a prey-oriented fishery with low prey catchability gives more yield and resilience but in case of predator-oriented fishery with high predator catchability, gives more of these ecological services. Thus to get both the optimum yield and resilience, a balanced harvesting approach is needed between the prey and predator trophic levels. Throughout the analysis, we use both the analytical as well as numerical techniques.
Divine Wanduku, B.O. Oluyede
Nonlinear Analysis: Modelling and Control, Volume 25, pp 461–481-461–481; doi:10.15388/namc.2020.25.16660

This paper presents the dynamics of mosquitoes and humans with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. The BRN R0* and ESPR E(e–(μvT1+μT2)) are computed. Conditions for deterministic extinction and permanence are expressed in terms of R0* and E(e–(μvT1+μT2)) and applied to a P. vivax malaria scenario. Numerical results are given.
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