In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of const...In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of constant equilibria.It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium,but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium.We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis,which imply that the prey-taxis plays an important role in the dynamics.展开更多
1 Introduction Boolean functions have important applications in stream ciphers and block ciphers.Over the last decades,the constructions of cryptographic Boolean functions have paid a lot of attention[1,2].Direct sum ...1 Introduction Boolean functions have important applications in stream ciphers and block ciphers.Over the last decades,the constructions of cryptographic Boolean functions have paid a lot of attention[1,2].Direct sum is a well-known secondary construction of cryptographic functions[3].By using the direct sum,a lot of functions with high nonlinearities can be obtained[4,5].However,the direct sum of two functions are decomposable functions,which have numerous null secondorder derivatives(which represents a potential weakness with respect to the higher order differential attack)[6].(In)decomposable functions were also studied in[7]by Zheng and Zhang under the name(non)separable functions.They provided some sufficient conditions that the functions are indecomposable[7].展开更多
基金supported by the Natural Science Foundation of Shandong Province,China(Nos.ZR2021MA028 and ZR2021MA025).
文摘In this paper,we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition.We first analyze the influence of prey-taxis on the local stability of constant equilibria.It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium,but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium.We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis,which imply that the prey-taxis plays an important role in the dynamics.
基金This work was supported by the Fundamental Research Funds for the Central Universities of China(2015QNA38)the Natural Science Foundation of China(Grant No.61972400).
文摘1 Introduction Boolean functions have important applications in stream ciphers and block ciphers.Over the last decades,the constructions of cryptographic Boolean functions have paid a lot of attention[1,2].Direct sum is a well-known secondary construction of cryptographic functions[3].By using the direct sum,a lot of functions with high nonlinearities can be obtained[4,5].However,the direct sum of two functions are decomposable functions,which have numerous null secondorder derivatives(which represents a potential weakness with respect to the higher order differential attack)[6].(In)decomposable functions were also studied in[7]by Zheng and Zhang under the name(non)separable functions.They provided some sufficient conditions that the functions are indecomposable[7].
