190 citations · 716 across the 45 of their papers we have counts for
32 papers · 1 filter
Improved Matlab code for Lyapunov exponents of fractional order systems
Marius-F. Danca
This paper presents an improved Matlab routine, FO_LE, for the numerical computation of Lyapunov exponents of fractional-order systems modeled by Caputo's derivative. It is conceiv…
Memory principle of the Matlab code for Lyapunov Exponents of fractional order
Marius-F. Danca, Michal feckan
The paper presents two representative classes of Impulsive Fractional Differential Equations defined with generalized Caputoś derivative, with fixed lower limit and changing lower…
Approximation and decomposition of attractors of a Hopfield neural network system
Marius-F. Danca, Guanrong Chen
In this paper, the Parameter Switching (PS) algorithm is used to approximate numerically attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent sche…
Mandelbrot set as a particular Julia set of Fractional Order, echipotential lines and external rays of Mandelbrot and Julia sets of Fractional Order
Marius-F. Danca
In this paper it is shown analytically and computationally that the Mandelbrot set of integer order are particular cases of Julia sets of Caputo s like fractional order. Also the d…
Mandelbrot set and Julia sets of fractional order
Marius-F. Danca, Michal Feckan
In this paper the fractional-order Mandelbrot and Julia sets in the sense of -th Caputo-like discrete fractional differences, for , are introduced and several propert…
Hidden and self-exited attractors in a heterogeneous Cournot oligopoly model
Marius-F. Danca, Marek Lampart
In this paper it is numerically proved that a heterogeneous Cournot oligopoly model presents hidden and self-excited attractors. The system has a single equilibrium and a line of e…
Rich dynamics and anticontrol of extinction in a prey-predator system
Marius-F. Danca, Michal Feckan, Nikolay Kuznetsov +1
This paper reveals some new and rich dynamics of a two-dimensional prey-predator system and to anticontrol the extinction of one of the species. For a particular value of the bifur…
Chaos control in the fractional order logistic map via impulses
Marius-F. Danca, Michal Feckan, Nikolay Kuznetsov
In this paper the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of f…
Approximating hidden chaotic attractors via parameter switching
Marius-F. Danca, Nikolay Kuznetsovc, Guanrong Chen
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The Parameter Switching (PS) algorithm is utilized, w…
Graphical structure of attraction basins of hidden attractors: the Rabinovich-Fabrikant system
Marius-F. Danca, Paul Bourke, Nikolay Kuznetsov
For systems with hidden attractors and unstable equilibria, the property that hidden attractors are not connected with unstable equilibria is now accepted as one of their main char…
Hidden chaotic attractors and chaos suppression in an impulsive discrete economical supply and demand dynamical system
M. -F. Danca, M. Feckan
Impulsive control is used to suppress the chaotic behavior in an one-dimensional discrete supply and demand dynamical system. By perturbing periodically the state variable with con…
Hidden chaotic attractors in fractional-order systems
Marius-F. Danca
In this paper, we present a scheme for uncovering hidden chaotic attrac- tors in nonlinear autonomous systems of fractional order. The stability of equilibria of fractional-order s…
Transient hidden chaotic attractors in a Hopfield neural system
Marius-F. Danca, Nikolay Kuznetsov
In this letter we unveil the existence of transient hidden coexisting chaotic attractors, in a simplified Hopfield neural network with three neurons.
Chaos control of Hastings-Powell model by combining chaotic motions
Marius-F. Danca, Joydev Chattopadhyay
In this paper, we propose a Parameter Switching (PS) algorithm as a new chaos control method for the Hastings-Powell (HP) system. The PS algorithm is a convergent scheme that switc…
Hidden transient chaotic attractors of Rabinovich-Fabrikant system
Marius-F. Danca
In [1], it is shown that the Rabinovich-Fabrikant (RF) system admits self-excited and hidden chaotic attractors. In this paper, we further show that the RF system also admits a pai…
Parameter Switching Synchronization
Marius-F. Danca, Nikolay Kuznetsov
In this paper we show how the Parameter Switching algorithm, utilized initially to approximate attractors of a general class of nonlinear dynamical systems, can be utilized also as…
Note on a parameter switching method for nonlinear ODEs
Marius-F. Danca, Michal Feckan
In this paper we study analytically a parameter switching (PS) algorithm applied to a class of systems of ODE, depending on a single real parameter. The algorithm allows the numeri…
Unusual dynamics and hidden attractors of the Rabinovich-Fabrikant system
Marius-F. Danca, Nikolay Kuznetsov, Guanrong Chen
This paper presents some unusual dynamics of the Rabinovich-Fabrikant system, such as "virtual" saddles, "tornado"-like stable cycles and hidden chaotic attractors. Due to the stro…
Looking more closely to the Rabinovich-Fabrikant system
Marius-F. Danca, Michal Feckan, Nikolay Kuznetsov +1
Recently, we look more closely into the Rabinovich-Fabrikant system, after a decade of the study in [Danca & Chen, 2004], discovering some new characteristics such as cycling chaos…
Breaking Points in Quartic Maps
M. Romera, G. Pastor, M. -F. Danca +3
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is…
Parameter switching in a generalized Duffing system: Finding the stable attractors
Marius-F. Danca, Nicolae Lung
This paper presents a simple periodic parameter-switching method which can find any stable limit cycle that can be numerically approximated in a generalized Duffing system. In this…
Lyapunov exponents of a class of piecewise continuous systems of fractional order
Marius-F. Danca
In this paper, we prove that a class of autonomous piecewise continuous systems of fractional order has well-defined Lyapunov exponents. For this purpose, based on some known resul…
Suppressing chaos in discontinuous systems of fractional order by active control
Marius-F Danca, Roberto Garrappa
In this paper, a chaos control algorithm for a class of piece-wise continuous chaotic systems of fractional order, in the Caputo sense, is proposed. With the aid of Filippov's conv…
Synchronization of piece-wise continuous systems of fractional order
Marius-F. Danca
The aim of this study is to prove analytically that synchronization of a piece-wise continuous class of systems of fractional order can be achieved. Based on our knowledge, there a…