Bogdanov-Takens bifurcation of codimension 33 in the Gierer-Meinhardt model

Bifurcation of the local Gierer-Meinhardt model is analyzed in this paper. It is found that the degenerate Bogdanov-Takens bifurcation of codimension 3 happens in the model, except that teh saddle-node bifurcation and the Hopf bifurcation. That was not reported in the existing results about this model. The existence of equilibria, their stability, the bifurcation and the induced complicated and interesting dynamics are explored in detail, by using the stability analysis, the normal form method and bifurcation theory. Numerical results are also presented to validate theoretical results

Synchronization of a class of fractional-order neural networks with multiple time delays by comparison principles

This paper studies the synchronization of fractional-order neural networks with multiple time delays. Based on an inequality of fractional-order and comparison principles of linear fractional equation with multiple time delays, some sufficient conditions for synchronization of master-slave systems are obtained. Example and related simulations are given to demonstrate the feasibility of the theoretical results

On sensitivity analysis of parameters for fractional differential equations with Caputo derivatives

In this paper, we discuss the effect of parameter variations on the performance of fractional differential equations and give the concept of fractional sensitivity functions and fractional sensitivity equations. Meanwhile, by employing Laplace transform and the inverse Laplace transform, some main results on fractional differential equations are proposed. Finally, two simple examples with numerical simulations are provided to show the validity and feasibility of the proposed theorem

On sensitivity analysis of parameters for fractional differential equations with Caputo derivatives

In this paper, we discuss the effect of parameter variations on the performance of fractional differential equations and give the concept of fractional sensitivity functions and fractional sensitivity equations. Meanwhile, by employing Laplace transform and the inverse Laplace transform, some main results on fractional differential equations are proposed. Finally, two simple examples with numerical simulations are provided to show the validity and feasibility of the proposed theorem

Boundary value problems of hybrid fractional integro-differential systems involving the conformable fractional derivative

In this paper, we study a boundary value problem for the hybrid fractional integro-differential system involving the conformable fractional derivative. We first discuss the existence of solutions using the Krasnoselskii fixed point theorem. The second result will be the existence and uniqueness of solution and we obtain it using the Banach fixed point theorem. Finally, we end our work with an example to illustrate our results

Complete Convergence of the Maximum Partial Sums for Arrays of Rowwise of AANA Random Variables

The limiting behavior of the maximum partial sums | is investigated, and some new results are obtained, where { , ≥ 1, ≥ 1} is an array of rowwise AANA random variables and { , ≥ 1} is a sequence of positive real numbers. As an application, the Chung-type strong law of large numbers for arrays of rowwise AANA random variables is obtained. The results extend and improve the corresponding ones of Hu and Taylor (1997) for arrays of rowwise independent random variables

Variable coefficient fractional‐order PID controller and its application to a SEPIC device

The fractional-order proportional–integral–derivative (FOPID) controller has two more parameters than the integer-order proportional–integral–derivative (PID). Such characteristic makes the controller design more flexible and leads to superior performance. This study proposes a variable coefficient FOPID (VCFOPID) with optimal single step parameters, combining discrete synthesis and variable control parameters. The new algorithm is compared with previous FOPID discrete methods via several examples. Since the energy losses of the single-ended primary-inductor converter (SEPIC) cannot be ignored, the standard models are insufficient and a new model is derived using quantum-behaved particle swarm optimisation. The VCFOPID is applied to the SEPIC and both the effectiveness of the controller and the model are verified experimentally.The authors would like to thank the anonymous reviewers for their constructive comments, which greatly improved the quality of this paper. This work was supported by the National Natural Science Funds of China (nos. 61403115 and 11971032).info:eu-repo/semantics/publishedVersio