Nonlinear Analysis: Modelling and Control <p>Founded in 1997. Journal provides a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature.&nbsp;</p> Vilnius University Press en-US Nonlinear Analysis: Modelling and Control 1392-5113 <p>Please read the Copyright Notice in&nbsp;<a href="">Journal Policy</a>.&nbsp;</p> Speech emotion classification using fractal dimension-based features <p>During the last 10–20 years, a great deal of new ideas have been proposed to improve the accuracy of speech emotion recognition: e.g., effective feature sets, complex classification schemes, and multi-modal data acquisition. Nevertheless, speech emotion recognition is still the task in limited success. Considering the nonlinear and fluctuating nature of the emotional speech, in this paper, we present fractal dimension-based features for speech emotion classification. We employed Katz, Castiglioni, Higuchi, and Hurst exponent-based features and their statistical functionals to establish the 224-dimensional full feature set. The dimension was downsized by applying the Sequential Forward Selection technique. The results of experimental study show a clear superiority of fractal dimension-based feature sets against the acoustic ones. The average accuracy of 96.5% was obtained using the reduced feature sets. The feature selection enabled us to obtain the 4-dimensional and 8-dimensional sets for Lithuanian and German emotions, respectively.</p> Gintautas Tamulevičius Rasa Karbauskaitė Gintautas Dzemyda ##submission.copyrightStatement## 2019-09-26 2019-09-26 24 5 679–695 679–695 10.15388/NA.2019.5.1 Multiobjective nonfragile fuzzy control for nonlinear stochastic financial systems with mixed time delays <p>In this study, a multiobjective nonfragile control is proposed for a class of stochastic Takagi and Sugeno (T–S) fuzzy systems with mixed time delays to guarantee the optimal <em>H</em><sub>2</sub> and <em>H</em><sub>∞</sub> performance simultaneously. Firstly, based on the T–S fuzzy model, two form of nonfragile state feedback controllers are designed to stabilize the T–S fuzzy system, that is to say, nonfragile state feedback controllers minimize the <em>H</em><sub>2</sub> and <em>H</em><sub>∞</sub> performance simultaneously. Then, by applying T–S fuzzy approach, the multiobjective <em>H</em><sub>2</sub>/<em>H</em><sub>∞</sub> nonfragile fuzzy control problem is transformed into linear matrix inequality (LMI)-constrained multiobjective problem (MOP). In addition, we efficiently solve Pareto optimal solutions for the MOP by employing LMI-based multiobjective evolution algorithm (MOEA). Finally, the validity of this approach is illustrated by a realistic design example.</p> Yang Yang Jianwei Xia Jianli Zhao Xiaodi Li Zhen Wang ##submission.copyrightStatement## 2019-09-26 2019-09-26 24 5 696–717 696–717 10.15388/NA.2019.5.2 Feedback control and its impact on generalist predator–prey system with prey harvesting <p>This article examines the effectiveness of feedback control as a management policy on a generalist predator–prey system with prey harvesting. We discuss the result of implementing feedback control with respect to prey and predator separately. This paper also depicts the effect of exploitations up to maximum sustainable yield (MSY). We observe that with a constant fishing effort MSY policy is a sustainable management policy to protect both the species. However, further increase of fishing effort may cause the extinction of prey species. But considering feedback control of fishing effort may restrict the extinction of prey species. When fishing effort is controlled in terms of prey density, the extinction of prey population can be avoided. In this case, there may be coexistences of prey, predator and fishery or extinction of fishery. But when fishing effort is controlled by predator density, it is difficult to manage the coexistences of prey, predator and fishery.</p> <p>&nbsp;</p> Debabrata Das Tapan Kumar Kar ##submission.copyrightStatement## 2019-09-26 2019-09-26 24 5 718–732 718–732 10.15388/NA.2019.5.3 Infinite point and Riemann–Stieltjes integral conditions for an integro-differential equation <p>In this paper, we study the existence of solutions for two nonlocal problems of&nbsp;integro-differential equation with nonlocal infinite-point and Riemann–Stieltjes integral boundary&nbsp;conditions. The continuous dependence of the solution will be studied.<br><br></p> <p>&nbsp;</p> Ahmed El-Sayed Reda Gamal ##submission.copyrightStatement## 2019-09-26 2019-09-26 24 5 733–754 733–754 10.15388/NA.2019.5.4 Spectrum curves for a discrete Sturm–Liouville problem with one integral boundary condition <p>This paper presents new results on the spectrum on complex plane for discrete Sturm–Liouville problem with one integral type nonlocal boundary condition depending on three parameters: <em>γ</em>, <em>ξ</em><sub>1</sub> and <em>ξ</em><sub>2</sub>. The integral condition is approximated by the trapezoidal rule. The dependence on parameter γ is investigated by using characteristic function method and analysing spectrum curves which gives qualitative view of the spectrum for fixed <em>ξ</em><sub>1&nbsp;</sub>= <em>m</em><sub>1&nbsp;</sub>/ <em>n</em> and <em>ξ</em><sub>2</sub> = <em>m</em><sub>2</sub> / <em>n</em>, where <em>n</em> is discretisation parameter. Some properties of the spectrum curves are formulated and illustrated in figures for various <em>ξ</em><sub>1</sub> and <em>ξ</em><sub>2</sub>.</p> <p><span style="display: inline !important; float: none; background-color: #ffffff; color: #000000; cursor: text; font-family: 'Noto Sans',Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">*The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).</span></p> Kristina Bingelė Agnė Bankauskienė Artūras Štikonas ##submission.copyrightStatement## 2019-09-26 2019-09-26 24 5 755–774 755–774 10.15388/NA.2019.5.5 Global attracting solutions to Hilfer fractional differential inclusions of Sobolev type with noninstantaneous impulses and nonlocal conditions <p>In this paper, we establish the existence of decay mild solutions on an unbounded&nbsp;interval of nonlocal fractional semilinear differential inclusions with noninstantaneous impulses&nbsp;and involving the Hilfer derivative. Our argument uses fixed point theorems, semigroup theory,&nbsp;multi-functions and a measure of noncompactness on the space of piecewise weighted continuous&nbsp;functions defined on an unbounded interval. An example is provided to illustrate our results.</p> JinRong Wang Ahmed Gamal Ibrahim Donal O’Regan ##submission.copyrightStatement## 2019-09-26 2019-09-26 24 5 775–803 775–803 10.15388/NA.2019.5.6 Time-delayed impulsive control for discrete-time nonlinear systems with actuator saturation <p>This paper focuses on the problem of time-delayed impulsive control with actuator&nbsp;saturation for discrete-time dynamical systems. By establishing a delayed impulsive difference&nbsp;inequality, combining with convex analysis and inequality techniques, some sufficient conditions&nbsp;are obtained to ensure exponential stability for discrete-time dynamical systems via time-delayed&nbsp;impulsive controller with actuator saturation. The designed controller admits the existence of some&nbsp;transmission delays in impulsive feedback law, and the control input variables are required to&nbsp;stay within an availability zone. Several numerical simulations are also given to demonstrate the&nbsp;effectiveness of the proposed results.&nbsp;</p> Liangliang Li Chuandong Li Wei Zhang ##submission.copyrightStatement## 2019-09-26 2019-09-26 24 5 804–818 804–818 10.15388/NA.2019.5.7 Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces <p>In this paper, we introduce the concept of enhanced probabilistic metric space (briefly&nbsp;EPM-space) as a type of probabilistic metric space. Also, we investigate the existence of fixed points&nbsp;for a (finite or infinite) linear combination of different types of contractive mappings in EPM-spaces.&nbsp;Furthermore, we investigate about the convergence of sequences (generated by a finite or infinite&nbsp;family of contractive mappings) to a common fixed point. The useful application of this research is&nbsp;the study of the stability of switched dynamic systems, where we study the conditions under which&nbsp;the iterative sequences generated by a (finite or infinite) linear combination of mappings (contractive&nbsp;or not), converge to the fixed point. Also, some examples are given to support the obtained results.&nbsp;In the end, a number of figures give us an overview of the examples.</p> Shahnaz Jafari Maryam Shams Asier Ibeas Manuel De La Sen ##submission.copyrightStatement## 2019-09-26 2019-09-26 24 5 819–837 819–837 10.15388/NA.2019.5.8 Modeling the uptake of fluorescent molecules into 3D cellular spheroids <p>Three mathematical models were developed to analyze the dynamics of fluorescent dyes&nbsp;penetration into 3D cellular spheroids. Two fluorescent dyes were chosen to verify mathematical&nbsp;models: rhodamine 6G (R6G) as a&nbsp;small molecule, which can freely penetrate through the cells,&nbsp;and wheat germ agglutinin (WGA) conjugated with Alexa488 fluorescent label, which reacts with&nbsp;the cells plasma membrane, and its cellular penetration is significantly lower. Dye penetration and&nbsp;binding to cells were modeled with nonlinear diffusion–reaction equations. System of differential&nbsp;equations was solved using numerical methods, and good correspondence with physical experiment&nbsp;was shown. Diffusion coefficients in extracellular matrix were determined for both fluorescent dyes,&nbsp;and the influence of reactions parameters to WGA penetration was analyzed. Dynamics of dyes&nbsp;accumulation into cell spheroids were also determined.</p> Rokas Astrauskas Feliksas Ivanauskas Greta Jarockytė Vitalijus Karabanovas Ričardas Rotomskis ##submission.copyrightStatement## 2019-09-26 2019-09-26 24 5 838–852 838–852 10.15388/NA.2019.5.9