In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PD^σ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

Whale optimization algorithm, as a relatively novel swarm-based intelligence optimization algorithm, has been extensively utilized in numerous scientific and engineering fields. The intent of this work was to devise a modified WOA based on multi-strategy, named MSWOA, to address somewhat deficiencies of the original WOA, such as converging slowly, stagnating at local minima and poor stability. First, a tent map function is adopted to optimize the distribution of the initial population in problem domain. Second, new iteration-based update strategies of convergence factor and inertia weight are constructed to regulate the balance between global and local search capabilities and improve the optimization ability. Additionally, an optimal feedback strategy is presented in the search for prey stage to enhance the global search ability. Numerical experimental results based on 24 test benchmark functions reveal that the proposed MSWOA significantly improves the standard WOA in terms of solution accuracy and convergence speed, and outperforms the comparison algorithms. Furthermore, the results show that the inertia weight strategy has the greatest effect on the performance of basic WOA performance, followed by the convergence factor, and then the optimal feedback strategy.

As an efficient meta-heuristic algorithm, the whale optimization algorithm (WOA) has been extensively applied to practical problems. However, WOA still has the drawbacks of converging slowly, and jumping out from extreme points especially for large scale optimization problems. To overcome these defects, a modified whale optimization algorithm integrated with a crisscross optimization algorithm (MWOA-CS) is proposed. In MWOA-CS, each dimension of the optimization problem updates its position by randomly performing improved WOA or crisscross optimization algorithm during the entire iterative process. The improved WOA adopts the new nonlinear convergence factor and nonlinear inertia weight to tune the ability of exploitation and exploration. To analyze the performance of MWOA-CS, a series of numerical experiments were performed on 30 test benchmark functions with dimension ranging from 300 to 1000. The experimental results revealed that the presented MWOA-CS provided better convergence speed and accuracy, and meanwhile, displayed a significantly more effective and robust performance than the original WOA and other state of the art meta-heuristic algorithms for solving large scale global optimization problems.