A model for the amount of pollution in lakes connected with some rivers is introduced.In this model,it is supposed the density of pollution in a lake has memory.The model leads to a system of fractional differential e...A model for the amount of pollution in lakes connected with some rivers is introduced.In this model,it is supposed the density of pollution in a lake has memory.The model leads to a system of fractional differential equations.This system is transformed into a system of Volterra integral equations with memory kernels.The existence and regularity of the solutions are investigated.A high-order numerical method is introduced and analyzed and compared with an explicit method based on the regularity of the solution.Validation examples are supported,and some models are simulated and discussed.展开更多
The fractional logistic map holds rich dynamics and is adopted to generate chaotic series.A watermark image is then encrypted and inserted into the original images.Since the encryption image takes the fractional order...The fractional logistic map holds rich dynamics and is adopted to generate chaotic series.A watermark image is then encrypted and inserted into the original images.Since the encryption image takes the fractional order within[0,1],it increases the key space and becomes difficult to attack.This study provides a robust watermark method in the protection of the copyright of hardware,images,and other electronic files.展开更多
文摘A model for the amount of pollution in lakes connected with some rivers is introduced.In this model,it is supposed the density of pollution in a lake has memory.The model leads to a system of fractional differential equations.This system is transformed into a system of Volterra integral equations with memory kernels.The existence and regularity of the solutions are investigated.A high-order numerical method is introduced and analyzed and compared with an explicit method based on the regularity of the solution.Validation examples are supported,and some models are simulated and discussed.
基金Project supported by the Sichuan Science and Technology Support Program,China(No.2018JY0120)。
文摘The fractional logistic map holds rich dynamics and is adopted to generate chaotic series.A watermark image is then encrypted and inserted into the original images.Since the encryption image takes the fractional order within[0,1],it increases the key space and becomes difficult to attack.This study provides a robust watermark method in the protection of the copyright of hardware,images,and other electronic files.
