## About

100

Publications

15,370

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

1,471

Citations

Citations since 2016

Introduction

My current research focuses on the qualitative and quantitative analysis of systems of fractional-order differential equations, as well as systems of delay differential equations with distributed delays. I am interested in several application fields, such as neuroscience, medicine, biology and economy.

Additional affiliations

August 2010 - August 2020

**Institute e-Austria Timisoara**

Position

- Researcher

October 2003 - September 2006

April 2003 - present

## Publications

Publications (100)

This Special Issue will focus on the latest developments in the field of fractional differential equations and their systems. Investigators in the field are invited to present their original, unpublished papers on both theoretical and applied areas.
Topics of interest should include (but are not limited to):analysis of solutions of fractional diff...

We consider an infinite network of identical theta neurons, all-to-all coupled by instantaneous synapses. Using the Watanabe–Strogatz Ansatz, the mathematical model of this infinite network is reduced to a two-dimensional system of differential equations. We determine the number of equilibria of this reduced system with respect to two characteristi...

This paper is devoted to the analysis of a Cournot game, described by a nonlinear mathematical model with four distributed time delays, modelling the behavior of two interacting firms on the market. For each firm, a delay for its own production and one for the production of the competitor are introduced. The analysis of the stability of the four eq...

The aim of this work is to describe the dynamics of a fractional-order coupled FitzHugh–Nagumo neuronal model. The equilibrium states are analyzed in terms of their stability properties, both dependently and independently of the fractional orders of the Caputo derivatives, based on recently established theoretical results. Numerical simulations are...

The present paper proposes a five-dimensional mathematical model for studying the labor market, focusing on unemployment, migration, fixed term contractors, full time employment and the number of available vacancies. The distributed time delay is considered in the rate of change of available vacancies that depends on the past regular employment lev...

The traditional Wilson-Cowan model of excitatory and inhibitory meanfield interactions in neuronal populations considers a weak Gamma distribution of time delays when processing inputs, and is obtained via a time-coarse graining technique that averages the population response. Previous analyses of the stability of the Wilson-Cowan model focused on...

In this paper, is analyzed a mathematical model with two distributed time delays for the control of unemployment. The positivity and boundedness of the solutions of the considered mathematical model are analyzed, and the existence of a unique positive equilibrium state of the system is proved. It is shown that this equilibrium is locally asymptotic...

In this paper, a theoretical and numerical investigation is undertaken for a fractional-order version of the Rulkov neuronal model, involving Caputo fractional variable-order differences of convolution type. As the first step, using linearization techniques and the Z-transform method, sufficient conditions are explored which guarantee the stability...

Systems of fractional-order differential equations present stability properties which differ in a substantial way from those of systems of integer order. In this paper, a detailed analysis of the stability of linear systems of fractional differential equations with Caputo derivative is proposed. Starting from the well-known Matignon’s results on st...

A mathematical model with distributed time delay describing the labor market is investigated, focusing on the asymptotic stability of the unique positive equilibrium point. The positivity and boundedness of the solutions are proved and the local stability analysis reveals that the positive equilibrium point is asymptotically stable, regardless of t...

Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases, fractional-order-dependent as well as fractional-order-independent characterisations of stability and instability properties are obtain...

Linear autonomous incommensurate systems that consist of two fractional-order difference equations of Caputo-type are studied in terms of their asymptotic stability and instability properties. More precisely, the asymptotic stability of the considered linear system is fully characterized, in terms of the fractional orders of the considered Caputo-t...

Fractional derivatives of Prabhakar type are capturing an increasing interest since their ability to describe anomalous relaxation phenomena (in dielectrics and other fields) showing a simultaneous nonlocal and nonlinear behaviour. In this paper we study the asymptotic stability of systems of differential equations with the Prabhakar derivative, pr...

This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control sc...

Derivatives of fractional order are introduced in different ways: as left-inverse of the fractional integral or by generalizing the limit of the difference quotient defining integer-order derivatives. Although the two approaches lead (under standard smoothness assumptions) to equivalent operators, the first one does not involve the function at the...

Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases, fractional-order-dependent as well as fractional-order-independent characterisations of stability and instability properties are obtain...

Derivatives of fractional order are introduced in different ways: as left-inverse of the fractional integral or by generalizing the limit of the difference quotient defining integer-order derivatives. Although the two approaches lead (under standard smoothness assumptions) to equivalent operators, the first one does not involve the function at the...

This paper generalizes the existing minimal mathematical model of a given generic touristic site by including a distributed time-delay to reflect the whole past history of the number of tourists in their influence on the environment and capital flow. A stability and bifurcation analysis is carried out on the coexisting equilibria of the model, with...

This paper analyses a mathematical model with time delay for the labor force on a market. Three variables are taken into account: the number of unemployed and employed persons in the market and the number of new vacancies created by the government and the private sector, which is based on a past value of the unemployment number in the creation of n...

Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and fractional-order-independent stability and instability properties are fully characterized, in terms of the main...

Several fractional-order operators are available and an in-depth knowledge of the selected operator is necessary for the evaluation of fractional integrals and derivatives of even simple functions. In this paper, we reviewed some of the most commonly used operators and illustrated two approaches to generalize integer-order derivatives to fractional...

A generalization of the well-known Wilson-Cowan model of excitatory and inhibitory interactions in localized neuronal populations is presented, by taking into consideration distributed time delays. A stability and bifurcation analysis is undertaken for the generalized model, with respect to two characteristic parameters of the system. The stability...

A parallel numerical simulation algorithm is presented for fractional-order systems involving Caputo-type derivatives, based on the Adams-Bashforth-Moulton (ABM) predictor-corrector scheme. The parallel algorithm is implemented using several different approaches: a pure MPI version, a combination of MPI with OpenMP optimization and a memory saving...

The existence of multiple exponentially stable equilibrium states and periodic solutions is investigated for Hopfield-type quaternion-valued neural networks (QVNNs) with impulsive effects and both time-dependent and distributed delays. Employing Brouwer’s and Leray–Schauder’s fixed point theorems, suitable Lyapunov functionals and impulsive control...

Necessary and sufficient conditions are given for the asymptotic stability and instability of a two-dimensional incommensurate order autonomous linear system, which consists of a differential equation with a Caputo-type fractional order derivative and a classical first order differential equation. These conditions are expressed in terms of the elem...

A four-dimensional mathematical model of the hypothalamus-pituitary-adrenal (HPA) axis is investigated, incorporating the influence of the GR concentration and general feedback functions. The inclusion of distributed time delays provides a more realistic modeling approach, since the whole past history of the variables is taken into account. The pos...

For two-dimensional autonomous linear incommensurate fractional-order dynamical systems with Caputo derivatives of different orders, necessary and sufficient conditions are obtained for the asymptotic stability and instability of the null solution. These conditions are expressed in terms of the elements of the system's matrix, as well as of the fra...

A theoretical analysis of two- and three-dimensional fractional-order Hindmarsh-Rose neuronal models is presented, focusing on stability properties and occurrence of Hopf bifurcations, with respect to the fractional order of the system chosen as bifurcation parameter. With the aim of exemplifying and validating the theoretical results, numerical si...

This paper analyzes a four-dimensional model of the hypothalamic-pituitary-adrenal (HPA) axis that includes the influence of the glucocorticoid receptor in the pituitary. Due to the spatial separation between the hypothalamus, pituitary and adrenal glands, distributed time delays are introduced in the mathematical model. The existence of the positi...

In this paper, a delay differential equations (DDEs) model of leukemia is introduced and its dynamical properties are investigated in comparison with the modified fractional-order system where the Caputo's derivative is used. The model takes into account three types of division that a stem-like cell can undergo and cell competition between healthy...

This paper generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The existence of a unique equilibrium point of the mathematical models is proved and a local stability analysis is...

In this paper, a delay differential equations (DDEs) model of leukemia is introduced and its dynamical properties are investigated in comparison with the modified fractional-order system where the Caputo's derivative is used. The model takes into account three types of division that a stem-like cell can undergo and cell competition between healthy...

This paper analyzes a four-dimensional model of the hypothalamic-pituitary-adrenal (HPA) axis that includes the influence of the glucocorticoid receptor in the pituitary. Due to the spatial separation between the hypothalamus, pituitary and adrenal glands, distributed time delays are introduced in the mathematical model. The existence of the positi...

The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the network are derived, based on the complex system parameters and the fractional order of the system, considering simp...

The qualitative theory of fractional-order dynamical systems and it applications to the sciences and engineering is a recent focus of interest of many researchers. In addition to natural similarities that can be drawn between fractional- and integer-order derivatives and fractional- and integer-order dynamical systems, very important differences ar...

The guest editors of this special issue would like to express their thanks to the authors who have submitted papers for consideration and the referees of the submitted papers.

In this paper, several analytical and numerical approaches are presented for the stability analysis of linear fractional-order delay differential equations. The main focus of interest is asymptotic stability, but bounded-input bounded-output (BIBO) stability is also discussed. The applicability of the Laplace transform method for stability analysis...

A major impediment towards the industrial adoption of decentralized
distributed systems comes from the difficulty to theoretically prove that these
systems exhibit the required behavior. In this paper, we use probability theory
to analyze a decentralized auto-scaling algorithm in which each node
probabilistically decides to scale in or out. We prov...

Several topics related to the dynamics of fractional-order neural networks of Hopfield type are investigated, such as stability and multi-stability (coexistence of several different stable states), bifurcations and chaos. The stability domain of a steady state is completely characterized with respect to some characteristic parameters of the system,...

A cryptosystem is proposed, based on a class of chaotic discrete-time delayed Hopfield neural networks of two non-identical neurons with no self-connections previously analyzed by the authors [J. Nonlinear Sci. 18, No. 4, 415–432 (2008; Zbl 1169.37012)]. The security of this cryptosystem is discussed and some simulations are presented which illustr...

Using the Mellin transform approach, it is shown that, in contrast with
integer-order derivatives, the fractional-order derivative of a periodic
function cannot be a function with the same period. The three most widely used
definitions of fractional-order derivatives are taken into account, namely, the
Caputo, Riemann-Liouville and Grunwald-Letniko...

In this paper we discuss the stability analysis for fractional-order neural networks of Hopfield type. The stability domain of a steady state is completely characterized with respect to some characteristic parameters of the system, in the case of a two-dimensional network and of a network of n ≥ 3 neurons with ring structure. The values of the char...

In this paper we investigate multistability of Hopfield-type neural networks with distributed delays and impulses, by using Lyapunov functionals, stability theory and control by impulses. Example and simulation results are given to illustrate the effectiveness of the results.

In this paper we investigate multistability of discrete-time Hopfield-type neural networks with distributed delays and impulses, by using Lyapunov functionals, stability theory and control by impulses. Example and simulation results are given to illustrate the effectiveness of the results.

The existence of multiple periodic solutions and their exponential stability are investigated for impulsive hybrid Hopfield-type neural networks with both time-dependent and distributed delays, using the Leray–Schauder fixed point theorem and Lyapunov functionals. The criteria given are easily verifiable, possess many adjustable parameters, and dep...

In this paper, an impulsive control approach is presented for the projective synchro-nization of two different chaotic Hopfield-type discrete-time neural networks with delays. The global asymptotic stability of the error dynamical system is studied, using linear matrix in-equalities, vector Lyapunov functions and the stability theory of impulsive s...

The existence of an infinite chain of heteroclinic orbits connecting saddle-nodes is proved, in the case of a simplified system of differential equations governing the longitudinal flight of an aircraft, using fixed point theory for nonlinear Volterra operators with convolution kernels. Numerical simulations are given and the importance of the obta...

Impulsive synchronization results are presented for discrete-time neural networks with delay, using linear matrix inequality and vector Lyapunov function techniques. The synchronizing impulses are assumed to contain non-delayed, as well as delayed terms. An example is given to illustrate the effectiveness of the results.

In this paper, it is shown that when the automatic flight control system (AFCS) is decoupled, then on the path of longitudinal flight equilibria of the ALFLEX reentry vehicle, there exist saddle–node bifurcations resulting in oscillations: when the elevator angle exceeds the bifurcation value, the angle of attack and pitch rate oscillate with the s...

The motion around the center of mass of a rigid unmanned aircraft, whose flight control system fails, in an “Aero Data Model In a Research Environment” is described, by a set of nine nonlinear ordinary differential equations. The longitudinal flight with constant forward velocity is described by a subset of three nonlinear differential equations, o...

By means of coincidence degree theory and Mawhin's continuation theorem, a theoretical proof is given for the existence of oscillatory solutions of the simplified dynamical system which governs the motion around the center of mass in a longitudinal flight with constant forward velocity of a rigid aircraft, when the automatic flight control system i...

In this paper the oscillation susceptibility of an aircraft in a longitudinal flight with constant forward velocity is analyzed in different flight models. Conditions which ensure such a flight, and equations governing the flight are presented. The stability of the equilibriums appearing is analyzed and the existence of Hopf bifurcations and saddle...

This paper is devoted to the analysis of a discrete-time delayed Hopfield-type neural network of p ges 3 neurons with bidirectional ring architecture. The stability domain of the null solution is found, the values of the characteristic parameters for which bifurcations occur at the origin are identified and the existence of fold/cusp, Neimark-Sacke...

This paper is devoted to the analysis of a discrete-time-delayed Hopfield-type neural network of p neurons with ring architecture. The stability domain of the null solution is found, the values of the characteristic parameter for which bifurcations occur at the origin are identified and the existence of Fold/Cusp, Neimark-Sacker and Flip bifurcatio...

In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two different delays and self-connections. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these paramete...

A method for the construction of Lyapunov functions and the computation of regions of attraction is presented for the case of weak asymptotic stability in discrete dynamical systems.

Considering the linear delay difference system x(n+1)=ax(n)+Bx(n-k), where a∈(0,1), B is a p×p real matrix, and k is a positive integer, the stability domain of the null solution is completely characterized in terms of the eigenvalues of the matrix B. It is also shown that the stability domain becomes smaller as the delay increases. These results m...

This paper is devoted to the bifurcation analysis of a two-dimensional discrete-time delayed Hopfield-type neural network.
In the most general framework considered so far in the known literature, the stability domain of the null solution and the
bifurcations occurring at its boundary are described in terms of two characteristic parameters. By apply...

A complete bifurcation analysis has been presented for a discrete-time Hopfield-type neural network of two neurons with several delays, uncovering the structure of the stability domain of the null solution, as well as the types of bifurcations occurring at its boundary. The numerical example illustrated the theoretical results and suggested some ro...

A bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two delays, two internal
decays and no self-connections, choosing the product of the interconnection coefficients as the characteristic parameter for
the system. The stability domain of the null solution is found, the values of the characteristic pa...

In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network with a single delay. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, fold or Neimark–Sacker bifurcations oc...

It is shown that the simplified system of differential equations that governs the motion of the automatic-landing flight-experiment (ALFLEX) reentry vehicle is neither structurally stable, nor topologically equivalent to the general dynamical system governing the same motion. Hence, the general and the simplified mathematical models of ALFLEX give...

In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two different delays and self-connections. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these paramete...

The dependence of the steady states on the external input vector I for the continuous-time and discrete-time Hopfield-type neural networks of n neurons is discussed. Conditions for the existence of one or several paths of steady states are derived. It is shown that, in some conditions, for an external input I there may exist at least 2n exponential...

A method for determination and two methods for approximation of the domain of attraction D a ( 0 ) of the asymptotically stable zero steady state of an autonomous, ℝ -analytical, discrete dynamical system are presented. The method of determination is based on the construction of a Lyapunov function V , whose domain of analyticity is D a ( 0 ) . The...