Chaos, Solitons and Fractals: X最新文献

The generation of high-order rogue waves (RWs) without the exact solution is an intriguing subject that has not yet been fully explored, especially for the third-order RWs. In this paper, we investigate the collision dynamics in a three-component Bose–Einstein condensate (BEC), and propose a scheme capable of generating such high-order RWs, such as second- and third-order RWs. The results show that the peaks of the three first-order RWs coincide in time and space when the third-order RWs are excited during the collision. Furthermore, by controlling the offsets of initial wavepackets and intraspecific interaction coefficients within the BEC, the collision behavior of RWs can be precisely manipulated. Compared to two-component BECs, these three-component collisions exhibit more diverse structures for exciting RW phenomena.

Riccati’s differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati’s differential equation with the Cole–Hopf transform shows a relation between the first order evolution equations and the second order evolution equations, its generalization suggests the existence of recurrence formula leading to a sequence of differential equations with different order. In conclusion, by means of the logarithmic representation of operators, a transform between the first order evolution equations and the higher order evolution equation is presented. Several classes of evolution equations with different orders are given, and some of them are shown as examples.

The aim of this paper is to explore finite-time synchronization in a specific subset of fractional-order epidemic reaction–diffusion systems. Initially, we introduce a new lemma for finite-time stability, which extends existing criteria and builds upon previous discoveries. Following this, we design effective state-dependent linear controllers. By utilizing a Lyapunov function, we derive new sufficient conditions to ensure finite-time synchronization within a predefined time frame. Lastly, we present numerical simulations to demonstrate the applicability and effectiveness of the proposed technique.

Unemployment is a major problem worldwide and is one of the key factors determining a nation’s economic status. The issue of unemployment is made more difficult globally by the ongoing rise in labor force participation and the scarcity of job positions. In this work, we study the unemployment model with two distinct fractional-order derivatives: the Caputo operator and the Atangana–Baleanu operator in the sense of Caputo (ABC). These derivatives under consideration are the operators widely utilized in modeling real-world phenomena in fractional dynamics. The existence and uniqueness of the solutions to the fractional model under consideration are ascertained using the fixed-point theory. The Hyers-Ulam analysis is employed to determine stability. For the numerical results, we present an Adams-type predictor–corrector (PC) technique for Caputo derivative and an extended Adams Bashforth (ABM) method for Atangana–Baleanu derivative. The outcomes achieved with the Atangana–Baleanu–Caputo and Caputo derivatives are identical to those of the regular case when fractional order $\nu =1.00$. However, the results obtained change slightly as fractional order assumes values smaller than one, and this variation becomes most noticeable when the fractional order $\nu <0.72$. This is because of the fractional derivative definitions’ underlying kernel. It is shown that the Mittag–Leffler kernel derivative provides better results for smaller fractional orders.