On the Dynamics of a Model with Coexistence of Three Attractors: A Point,a Periodic Orbit and a Strange Attractor

For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. We study using analytic tools the dynamics of such system. We describe its global dynamics near the infinity, and prove that it has no Darboux first integrals.     

The continuous time random walk,still trendy: fifty-year history,state of art and outlook

In this article we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism, the numerous modifications permitted by its flexibility, its various applications, and the promising perspectives in the various fields of knowledge. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We focused on a pivotal role of CTRWs mainly in anomalous stochastic processes discovered in physics and beyond. This article plays the role of an extended announcement of the Eur. Phys. J. B Special Issue [http://epjb.epj.org/open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on] containing articles which show incredible possibilities of the CTRWs.     

Limit cycles bifurcating from a zero–Hopf singularity in arbitrary dimension

Nonlinear Dynamics - For a $$C^{m+1}$$ differential system on $$\mathbb {R}^n$$ , we study the limit cycles that can bifurcate from a zero–Hopf singularity, i.e., from a singularity with...     

The symmetric periodic orbits for the two-electron atom

We analyse the existence of symmetric periodic orbits of the two-electron atom. The results obtained show that there exist six families of periodic orbits that can be prolonged from a continuum of periodic symmetric orbits. The main technique applied in this study is the continuation method of Poincaré.     

Number of Invariant Straight Lines for Homogeneous Polynomial Vector Fields of Arbitrary Degree and Dimension

We study the number of invariant straight lines through the origin of the homogeneous polynomial differential systems of degree m in \mathbb R^d{{\mathbb R}^d} or \mathbb C^d{{\mathbb C}^d} , when this number is finite. This notion extends in the natural way the classical notion of eigenvectors of homogeneous linear differential systems to homogeneous polynomial differential systems. This number provides un upper bound for the number of infinite singular points of the polynomial differential systems of degree m in \mathbb R^d{{\mathbb R}^d} . This upper bound is reached if all the invariant straight lines through the origin are real.     

Perylene π‐Bridges Equally Delocalize Anions and Cations: Proportioned Quinoidal and Aromatic Content

A complete experimental and theoretical study has been carried out for aromatic and quinoidal perylene‐based bridges substituted with bis(diarylamine) and bis(arylimine) groups respectively. The through‐bridge inter‐redox site electronic couplings (V_AB) have been calculated for their respective mixed‐valence radical cation and radical anion species. The unusual similitudes of the resulting V_AB values for the given structures reveal the intervention of molecular shapes with balanced semi‐quinoidal/semi‐aromatic structures in the charge delocalization. An identical molecular object equally responding to the injection of either positive or negative charges is rare in the field of organic π‐conjugated molecules. However, once probed herein for perylene‐based systems, it can be extrapolated to other π‐conjugated bridges. As a result, this work opens the door to the rational design of true ambipolar bulk and molecular conductors.     

Harnessing ICl reduction processes for synthesis of different BEDT-TTF-based molecular conductors

Both calculations and experimental data, showing the possibility of formation of I3-, I2Cl-, and ICl2- anions through ICl reduction processes, are described in detail. The above processes were used successfully for the preparation of different molecular conductors based on trihalide anions and bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF). The reaction between ICl and BEDT-TTF occurring in a strong polar reaction media (epsilon > or = 34.8 D) results in the formation of novel molecular conductors containing different sets of the I3-, I2Cl-, and ICl2- anions: beta-(BEDT-TTF)2[(I3)0.4(I2Cl)0.6], beta'BEDT-TTF)2[(I2Cl)0.2(ICl2)0.8], and beta' '-('-(BEDT-TTF)2[(I3)0.075(I2Cl)0.150(ICl2). These molecular conductors reveal semiconducting (beta'-phase) as well as metallic (beta- and beta' '-phases) transport properties. It is also shown that in the reaction media with polarity less than 18.4 D only the I3- anion is incorporated in the BEDT-TTF-based molecular crystals. This fact is an unexpected outcome of our study.     

A very bulky carboxylic perchlorotriphenylmethyl radical as a novel ligand for transition metal complexes. A new spin frustrated metal system

Reaction of a carboxylic perchlorotriphenylmethyl radical with Cu2(O2CCH3)(4).2H2O using different molar ratios yields two different transition metal complexes with strong intramolecular antiferromagnetic interactions, which in the case of complex 2 follows a butterfly spin frustrated model.