Dynamics of a diffusive predator–prey model with herd behavior

This paper is devoted to considering a diffusive predator–prey model with Leslie–Gower term and herd behavior subject to the homogeneous Neumann boundary conditions. Concretely, by choosing the proper bifurcation parameter, the local stability of constant equilibria of this model without diffusion and the existence of Hopf bifurcation are investigated by analyzing the distribution of the eigenvalues. Furthermore, the explicit formula for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are also derived by applying the normal form theory. Next, we show the stability of positive constant equilibrium, the existence and stability of periodic solutions near positive constant equilibrium for the diffusive model. Finally, some numerical simulations are carried out to support the analytical results

Design and analysis of bent functions using M\mathcal{M}-subspaces

In this article, we provide the first systematic analysis of bent functions $f$ on $\mathbb{F}_2^{n}$ in the Maiorana-McFarland class $\mathcal{MM}$ regarding the origin and cardinality of their $\mathcal{M}$-subspaces, i.e., vector subspaces on which the second-order derivatives of $f$ vanish. By imposing restrictions on permutations $\pi$ of $\mathbb{F}_2^{n/2}$, we specify the conditions, such that Maiorana-McFarland bent functions $f(x,y)=x\cdot \pi(y) + h(y)$ admit a unique $\mathcal{M}$-subspace of dimension $n/2$. On the other hand, we show that permutations $\pi$ with linear structures give rise to Maiorana-McFarland bent functions that do not have this property. In this way, we contribute to the classification of Maiorana-McFarland bent functions, since the number of $\mathcal{M}$-subspaces is invariant under equivalence. Additionally, we give several generic methods of specifying permutations $\pi$ so that $f\in\mathcal{MM}$ admits a unique $\mathcal{M}$-subspace. Most notably, using the knowledge about $\mathcal{M}$-subspaces, we show that using the bent 4-concatenation of four suitably chosen Maiorana-McFarland bent functions, one can in a generic manner generate bent functions on $\mathbb{F}_2^{n}$ outside the completed Maiorana-McFarland class $\mathcal{MM}^\#$ for any even $n\geq 8$. Remarkably, with our construction methods it is possible to obtain inequivalent bent functions on $\mathbb{F}_2^8$ not stemming from two primary classes, the partial spread class $\mathcal{PS}$ and $\mathcal{MM}$. In this way, we contribute to a better understanding of the origin of bent functions in eight variables, since only a small fraction, of which size is about $2^{76}$, stems from $\mathcal{PS}$ and $\mathcal{MM}$, whereas the total number of bent functions on $\mathbb{F}_2^8$ is approximately $2^{106}$

When does a bent concatenation not belong to the completed Maiorana-McFarland class?

Every Boolean bent function $f$ can be written either as a concatenation $f=f_1||f_2$ of two complementary semi-bent functions $f_1,f_2$; or as a concatenation $f=f_1||f_2||f_3||f_4$ of four Boolean functions $f_1,f_2,f_3,f_4$, all of which are simultaneously bent, semi-bent, or 5-valued spectra-functions. In this context, it is essential to ask: When does a bent concatenation $f$ (not) belong to the completed Maiorana-McFarland class $\mathcal{M}^\#$? In this article, we answer this question completely by providing a full characterization of the structure of $\mathcal{M}$-subspaces for the concatenation of the form $f=f_1||f_2$ and $f=f_1||f_2||f_3||f_4$, which allows us to specify the necessary and sufficient conditions so that $f$ is outside $\mathcal{M}^\#$. Based on these conditions, we propose several explicit design methods of specifying bent functions outside $\mathcal{M}^\#$ in the special case when $f=g||h||g||(h+1)$, where $g$ and $h$ are bent functions.Comment: This is the authors' version of the camera-ready version to be presented at the 2024 IEEE International Symposium on Information Theory (ISIT 2024

Hard Fault Analysis of Trivium

Fault analysis is a powerful attack to stream ciphers. Up to now, the major idea of fault analysis is to simplify the cipher system by injecting some soft faults. We call it soft fault analysis. As a hardware--oriented stream cipher, Trivium is weak under soft fault analysis. In this paper we consider another type of fault analysis of stream cipher, which is to simplify the cipher system by injecting some hard faults. We call it hard fault analysis. We present the following results about such attack to Trivium. In Case 1 with the probability not smaller than 0.2396, the attacker can obtain 69 bits of 80--bits--key. In Case 2 with the probability not smaller than 0.2291, the attacker can obtain all of 80--bits--key. In Case 3 with the probability not smaller than 0.2291, the attacker can partially solve the key. In Case 4 with non--neglectable probability, the attacker can obtain a simplified cipher, with smaller number of state bits and slower non--linearization procedure. In Case 5 with non--neglectable probability, the attacker can obtain another simplified cipher. Besides, these 5 cases can be checked out by observing the key--stream

Effect of supercritical CO2 extraction on pore characteristics of coal and its mechanism

Abundant pore space in coal is not only the place for the accumulation of coalbed methane (CBM), but also the tunnel for gas migration. In this study, five sets of coal samples before and after the second coalification were selected from the eastern margin of Ordos Basin to simulate supercritical CO2 (Sc-CO2) extraction in supercritical extraction equipment. The evolutions of pore structure and porosity were tested by mercury intrusion porosimetry and nuclear magnetic resonance spectroscopy to compare the changes of pore structure and porosity due to the Sc-CO2 extraction, and to explain the related mechanism. The results show that: (1) Pore volume, pore specific surface area, and connectivity characteristics changed significantly due to Sc-CO2 extraction, and the increment of pore volume and pore specific surface area presented a law of increase–decrease–increase with the increase in the coal rank, and the turning point was near the second coalification. (2) The porosity increment change trend due to Sc-CO2 extraction was increase–decrease–increase with increasing coal rank, and the turning point was again near the second coalification, which supports the mercury intrusion porosimetry results. (3) The changes were observed in the porosity characteristics due to Sc-CO2 extraction through pore-increasing and expanding effects. Before the second coalification, the pore-increasing and expanding effects co-existed in the micropores, and after the second coalification, the pore-expanding effect mainly existed in the transitional pores and above. (4) The variation model for the pore structure of coal due to Sc-CO2 extraction was established. The conclusions offer not only important theoretical significance for the CO2-enhanced CBM (CO2-ECBM) mechanism but also important significance for CO2-ECBM engineering