@article{MTMT:34037447,
	title = {General Exact Schemes for Second-Order Linear Differential Equations Using the Concept of Local Green Functions},
	url = {https://m2.mtmt.hu/api/publication/34037447},
	author = {Vizvári, Zoltán Ákos and Klincsik, Mihály and Odry, Péter and Tadity, Vladimir and Sári, Zoltán},
	doi = {10.3390/axioms12070633},
	journal-iso = {AXIOMS},
	journal = {AXIOMS},
	volume = {12},
	unique-id = {34037447},
	abstract = {In this paper, we introduce a special system of linear equations with a symmetric, tridiagonal matrix, whose solution vector contains the values of the analytical solution of the original ordinary differential equation (ODE) in grid points. Further, we present the derivation of an exact scheme for an arbitrary mesh grid and prove that its application can completely avoid other errors in discretization and numerical methods. The presented method is constructed on the basis of special local green functions, whose special properties provide the possibility to invert the differential operator of the ODE. Thus, the newly obtained results provide a general, exact solution method for the second-order ODE, which is also effective for obtaining the arbitrary grid, Dirichlet, and/or Neumann boundary conditions. Both the results obtained and the short case study confirm that the use of the exact scheme is efficient and straightforward even for ODEs with discontinuity functions.},
	year = {2023},
	eissn = {2075-1680}
}

@article{MTMT:33236539,
	title = {A competition system with nonlinear cross-diffusion: exact periodic patterns},
	url = {https://m2.mtmt.hu/api/publication/33236539},
	author = {Kersner, Róbert and Klincsik, Mihály and Zhanuzakova, Dinara},
	doi = {10.1007/s13398-022-01299-1},
	journal-iso = {RACSAM REV R ACAD A},
	journal = {REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS},
	volume = {116},
	unique-id = {33236539},
	issn = {1578-7303},
	abstract = {Our concern in this paper is to shed some additional light on the mechanism and the effect caused by the so called cross-diffusion. We consider a two-species reaction-diffusion (RD) system. Both "fluxes" contain the gradients of both unknown solutions. We show that-for some parameter range- there exist two different type of periodic stationary solutions. Using them, we are able to divide into parts the (eight-dimensional) parameter space and indicate the so called Turing domains where our solutions exist. The boundaries of these domains, in analogy with "bifurcation point", called "bifurcation surfaces". As it is commonly believed, these solutions are limits as t goes to infinity of the solutions of corresponding evolution system. In a forthcoming paper we shall give a detailed account about our numerical results concerning different kind of stability. Here we also show some numerical calculations making plausible that our solutions are in fact attractors with a large domain of attraction in the space of initial functions.},
	keywords = {pattern formation; Periodic stationary solutions; Stability of patterns; Cross-diffusion; Reaction-diffusion (RD )systems},
	year = {2022},
	eissn = {1579-1505}
}

@article{MTMT:27610269,
	title = {Persistence and Turing instability in a cross-diffusive predator-prey system with generalist predator},
	url = {https://m2.mtmt.hu/api/publication/27610269},
	author = {Miao, Baojun},
	doi = {10.1186/s13662-018-1676-x},
	journal-iso = {ADV DIFFER EQU-NY},
	journal = {ADVANCES IN DIFFERENCE EQUATIONS},
	unique-id = {27610269},
	issn = {1687-1839},
	year = {2018},
	eissn = {1687-1847}
}

@article{MTMT:26315221,
	title = {Effects of the self- and cross-diffusion on positive steady states for a generalized predator–prey system},
	url = {https://m2.mtmt.hu/api/publication/26315221},
	author = {Jia, Y and Xue, P},
	doi = {10.1016/j.nonrwa.2016.04.012},
	journal-iso = {NONLINEAR ANAL-REAL},
	journal = {NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS},
	volume = {32},
	unique-id = {26315221},
	issn = {1468-1218},
	year = {2016},
	eissn = {1878-5719},
	pages = {229-241}
}

@article{MTMT:26231019,
	title = {Turing instability for a competitor-competitor-mutualist model with nonlinear cross-diffusion effects},
	url = {https://m2.mtmt.hu/api/publication/26231019},
	author = {Wen, Zijuan and Fu, Shengmao},
	doi = {10.1016/j.chaos.2016.06.019},
	journal-iso = {CHAOS SOLITON FRACT},
	journal = {CHAOS SOLITONS & FRACTALS},
	volume = {91},
	unique-id = {26231019},
	issn = {0960-0779},
	year = {2016},
	eissn = {1873-2887},
	pages = {379-385}
}