In this paper, we study the bifurcation of nontrivial steady state solutions for a cross-diffusion prey-predator model with homogeneous Neumann boundary conditions. The existence of positive steady state solutions near a bifurcation point is proved using a crossing curve bifurcation theorem. We consider a situation where the transversality condition is not satisfied. Unlike the case in saddle-node bifurcation, the solution set is a pair of transversally intersecting curves.
 Q. Cao and J. Wu, Bifurcation solutions in the diffusive minimal sediment, Computers and Mathematics with Applications, 77 (2019), 888–906.
 M. G. Crandall and P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues ,and linearized stability, Arch.Ration. Mech. Anal., 52 (1973), 161–180.
 X. Feng, C. Li, H. Sun, and Y. Wang, Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and BD Functional Response, Complexity, 2021 (2021).
 L. Kong and F. Lu, Bifurcation branch of stationary solutions in a general predator-prey system with prey-taxis, Computers and Mathematics with Applications, 78 (2019), 191–203.
 Y. Jia, Y. Li, and J. Wu, Qualitative analysis on positive steady-states for an autocatalytic reaction model in thermodynamics, Discrete and Continuous Dynamical Systems, 37 (2017), 4785.
 C. Li, On global bifurcation for a cross-diffusion predator-prey system with prey-taxis, Computers and Mathematics with Applications, 76 (2018), 1014–1025.
 S. Li, J. Wu, and Y. Dong, Turing patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme, Journal of Differential Equations, 259 (2015), 1990–2029.
 S. Li, J. Wu, and H. Nie, Steady-state bifurcation and Hopf bifurcation for a diffusive Leslie-Gower predator-prey model, Computers and Mathematics with Applications, 70 (2015), 3043–3056.
 P. Liu and J. Shi, Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition, Journal of Differential Equations 264 (2018), 425–454.
 R. Memarbashi, A. Ghasemabadi, and Z. Ebadi, Backward bifurcation in a two strain model of heroin addiction, Computational Methods for Differential Equations 10 (2022), 656–673.
 K. Oeda and K. Kuto, Positive steady states for a prey-predator model with population flux by attractive transition, Nonlinear Analysis: Real World Applications, 44 (2018), 589–615.
 M. R. Patel, J. U. Pandya, and V. K. Patel, Numerical analysis of fluid flow behavior in two sided deep lid driven cavity using the finite volume technique, Computational Methods for Differential Equations, (2022).
 R. R. Patra, S. Kundu, and S. Maitra, Effect of delay and control on a predator-prey ecosystem with generalist predator and group defence in the prey species, The European Physical Journal Plus, 137 (2022), 28.
 M. Rudziva, O. A. Noreldin, P. Sibanda, and S. P. Goqo, A bifurcation analysis of multicomponent convection in a rotating low prandtl number fluid with internal heating, Applied and Computational Mathematics, 22 (2022), 78–100.
 X. Wang, J. Shi, and G. Zhang, Bifurcation and pattern formation in diffusive Klausmeier-Gray-Scott model of water-plant interaction, Journal of Mathematical Analysis and Applications, 497 (2021), 124860.
 Y. Wang, J. Wu, and Y. Jia, Steady-state bifurcation for a biological depletion model, International Journal of Bifurcation and Chaos, 26 (2016), 1650066.
 H. Xu and S. Fu, Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington- DeAngelis-type predator-prey model, Boundary Value Problems, 2019 (2019), 1–23.
 W. Zuo and J. Shi, Existence and stability of steady-state solutions of reaction-diffusion equations with nonlocal delay effect, Zeitschrift fu¨r angewandte Mathematik und Physik, 72 (2021), 1–26.
Farshid, M., Jalilian, Y. (2023). Steady state bifurcation in a cross diffusion prey-predator model. Computational Methods for Differential Equations, 11(2), 254-262. doi: 10.22034/cmde.2022.52663.2213
Marzieh Farshid; Yaghoub Jalilian. "Steady state bifurcation in a cross diffusion prey-predator model". Computational Methods for Differential Equations, 11, 2, 2023, 254-262. doi: 10.22034/cmde.2022.52663.2213
Farshid, M., Jalilian, Y. (2023). 'Steady state bifurcation in a cross diffusion prey-predator model', Computational Methods for Differential Equations, 11(2), pp. 254-262. doi: 10.22034/cmde.2022.52663.2213
Farshid, M., Jalilian, Y. Steady state bifurcation in a cross diffusion prey-predator model. Computational Methods for Differential Equations, 2023; 11(2): 254-262. doi: 10.22034/cmde.2022.52663.2213