68 citations · 337 across the 22 of their papers we have counts for
24 papers
Bifurcations and transition to chaos in generalized fractional maps of the orders 0 < alpha < 1
Mark Edelman, Avigayil B. Helman, Rasa Smidtaite
Generalized fractional maps of the orders 0 < alpha < 1 are Volterra difference equations of convolution type with kernels, which differences are absolutely summable, but the serie…
Stability of Fixed Points in Generalized Fractional Maps of the Orders
Mark Edelman
Caputo fractional (with power-law kernels) and fractional (delta) difference maps belong to a more widely defined class of generalized fractional maps, which are discrete convoluti…
Asymptotically periodic points, bifurcations, and transition to chaos in fractional difference maps
Mark Edelman, Avigayil Helman
In this paper, we derive analytic expressions for coefficients of the equations that allow calculations of asymptotically periodic points in fractional difference maps. Numerical s…
A note on stability of fractional logistic maps, Appl. Math. Lett. 125 (2022) 107787
Mark Edelman
In this paper, we show that the stability analysis in the paper A note on stability of fractional logistic maps, Appl. Math. Lett. 125 (2022) 107787 is incorrect and repeat a proof…
Asymptotic cycles in fractional maps of arbitrary positive orders
Mark Edelman, Avigayil B. Helman
Many natural and social systems possess power-law memory, and their mathematical modeling requires the application of discrete and continuous fractional calculus. Most of these sys…
Cycles in Asymptotically Stable and Chaotic Fractional Maps
Mark Edelman
The presence of the power-law memory is a significant feature of many natural (biological, physical, etc.) and social systems. Continuous and discrete fractional calculus is the in…