This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.

Yingqi Zhang

Caixia Liu

Xiaowu Mu

On Stochastic Finite-Time Control of Discrete-Time Fuzzy Systems with Packet Dropout

Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of <svg style="vertical-align:-0.20474pt;width:18.450001px;" id="M2" height="12.0625" version="1.1" viewBox="0 0 18.450001 12.0625" width="18.450001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,0,0,-.017,.062,11.738)"><use xlink:href="#x1D4B2" /></g></svg>-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.

Zhishuai Ding

Guifang Cheng

<svg style="vertical-align:-0.20474pt" height="12.0625" version="1.1" viewBox="0 0 18.450001 12.0625" width="18.450001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.738)"><path id="x1D4B2" d="M455 24l2 -2q66 26 128 97t139 204q126 219 183 291q58 73 113 73q22 0 36 -13t14 -34q0 -18 -12.5 -30.5t-30.5 -12.5q-43 0 -43 50h-1q-27 -7 -80 -88q-61 -92 -166 -273q-175 -301 -319 -301q-34 0 -46 4q85 79 141 233q44 124 99 214q56 93 138 179l-1 1
q-97 -16 -262 -312q-177 -319 -326 -319q-19 0 -47 6q30 24 59 72q26 42 44 85q21 49 44 111q56 151 192 287l-2 2q-17 -5 -36 -5q-48 0 -125 41q-76 42 -106 42q-47 0 -77.5 -29.5t-30.5 -71.5t24.5 -68t65.5 -26q37 0 65 20.5t56 65.5l16 -9q-54 -107 -139 -107
q-56 0 -92.5 35.5t-36.5 90.5q0 59 46 105t117 46q49 0 146 -49l36 -19q19 -12 40 -12q66 0 124 49l27 22l15 -16q-116 -115 -196 -321q-79 -205 -196 -310l2 -3q50 18 104 74q52 54 88 108q34 53 75 126q183 324 309 324q16 0 51 -11q-43 -31 -77 -96l-30 -57l-35 -79
l-31 -74q-92 -207 -195 -310z"/></g></svg>-Stability of Multistable Nonlinear Discrete-Time Systems

The dynamics of an impulsively controlled three-species food chain system with
the Beddington-DeAngelis functional response are investigated using the Floquet
theory and a comparison method. In the system, three species are prey, mid-predator,
and top-predator. Under an integrated control strategy in sense of biological and
chemical controls, the condition for extinction of the prey and the mid-predator
is investigated. In addition, the condition for extinction of only the mid-predator is
examined. We provide numerical simulations to substantiate the theoretical results.

Younghae Do

Hunki Baek

Dongseok Kim

Impulsive Perturbations of a Three-Species Food Chain System with the Beddington-DeAngelis Functional Response

This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both the <svg style="vertical-align:-3.50804pt;width:10.2px;" id="M1" height="13.3" version="1.1" viewBox="0 0 10.2 13.3" width="10.2" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,0,0,-.017,.062,8.863)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36&#xD;&#xA;t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" /></g></svg>th moment and almost sure exponential stability criteria are established by using the average impulsive interval. When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it means that the impulses should not happen too frequently. On the other hand, when the impulses are used to stabilize the system, an upper bound of average impulsive interval is derived; namely, enough impulses are needed to stabilize the system. The effectiveness of the proposed results is illustrated by two examples.

Xiaotai Wu

Litan Yan

Wenbing Zhang

Liang Chen

Exponential Stability of Impulsive Stochastic Delay Differential Systems

A discrete time two-nation arms race model involving a piecewise constant nonlinear control function is formulated and studied. By elementary but novel arguments, we are able to give a complete analysis of its asymptotic behavior when the threshold parameter in the control function varies from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>∞</mml:mi></mml:math>. We show that all solutions originated from positive initial values tend to limit one or two cycles. An implication is that when devastating weapons are involved, “terror equilibrium” can be achieved and escalated race avoided. It is hoped that our analysis will provide
motivation for further studying of discrete-time equations with piecewise smooth nonlinearities.

Chengmin Hou

Sui Sun Cheng

Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities

We investigate formulas for closely related series of the forms: <svg style="vertical-align:-3.8347pt;width:117.95px;" id="M1" height="17.4" version="1.1" viewBox="0 0 117.95 17.4" width="117.95"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,17.4)">
		<g transform="translate(72,-58.08)">
			<text transform="matrix(1,0,0,-1,-71.95,61.93)">
				<tspan style="font-size: 12.50px; " x="0" y="0">∑</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-60.52,68.19)">
				<tspan style="font-size: 8.75px; " x="0" y="0">∞</tspan>
				<tspan style="font-size: 8.75px; " x="0" y="9.9399996">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="4.3497438" y="9.9399996">=</tspan>
				<tspan style="font-size: 8.75px; " x="10.344864" y="9.9399996">0</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-43.22,61.95)">
				<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
				<tspan style="font-size: 12.50px; " x="6.2515001" y="0">/</tspan>
				<tspan style="font-size: 12.50px; " x="9.727334" y="0">(</tspan>
				<tspan style="font-size: 12.50px; " x="13.890833" y="0">𝑈</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-20.51,58.83)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑎</tspan>
				<tspan style="font-size: 8.75px; " x="4.3935041" y="0">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="8.743248" y="0">+</tspan>
				<tspan style="font-size: 8.75px; " x="14.738368" y="0">𝑏</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,1.62,61.95)">
				<tspan style="font-size: 12.50px; " x="0" y="0">+</tspan>
				<tspan style="font-size: 12.50px; " x="11.327718" y="0">𝑐</tspan>
				<tspan style="font-size: 12.50px; " x="16.516462" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg>, 
				<svg style="vertical-align:-3.8347pt;width:186.425px;" id="M2" height="18.762501" version="1.1" viewBox="0 0 186.425 18.762501" width="186.425"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,18.7625)">
		<g transform="translate(72,-56.99)">
			<text transform="matrix(1,0,0,-1,-71.95,60.84)">
				<tspan style="font-size: 12.50px; " x="0" y="0">∑</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-60.52,67.1)">
				<tspan style="font-size: 8.75px; " x="0" y="0">∞</tspan>
				<tspan style="font-size: 8.75px; " x="0" y="9.9399996">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="4.3497438" y="9.9399996">=</tspan>
				<tspan style="font-size: 8.75px; " x="10.344864" y="9.9399996">0</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-43.22,60.86)">
				<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
				<tspan style="font-size: 12.50px; " x="4.1634989" y="0">−</tspan>
				<tspan style="font-size: 12.50px; " x="12.728054" y="0">1</tspan>
				<tspan style="font-size: 12.50px; " x="18.979553" y="0">)</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-20.08,66.03)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-15.23,60.86)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑈</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-6.41,57.74)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑎</tspan>
				<tspan style="font-size: 8.75px; " x="4.3935041" y="0">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="8.743248" y="0">+</tspan>
				<tspan style="font-size: 8.75px; " x="14.738368" y="0">𝑏</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,12.94,60.86)">
				<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
				<tspan style="font-size: 12.50px; " x="3.4758339" y="0">(</tspan>
				<tspan style="font-size: 12.50px; " x="7.6393328" y="0">𝑈</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,29.39,57.74)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑎</tspan>
				<tspan style="font-size: 8.75px; " x="4.3935041" y="0">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="8.743248" y="0">+</tspan>
				<tspan style="font-size: 8.75px; " x="14.738368" y="0">𝑏</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,51.52,60.86)">
				<tspan style="font-size: 12.50px; " x="0" y="0">+</tspan>
				<tspan style="font-size: 12.50px; " x="11.340221" y="0">𝑐</tspan>
				<tspan style="font-size: 12.50px; " x="16.528967" y="0">)</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,72.22,66.03)">
				<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
			</text>

		</g>
	</g>
</svg>, 
				<svg style="vertical-align:-4.68874pt;width:164.1875px;" id="M3" height="22.9125" version="1.1" viewBox="0 0 164.1875 22.9125" width="164.1875"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,22.9125)">
		<g transform="translate(72,-53.67)">
			<text transform="matrix(1,0,0,-1,-71.95,58.37)">
				<tspan style="font-size: 12.50px; " x="0" y="0">∑</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-60.52,64.63)">
				<tspan style="font-size: 8.75px; " x="0" y="0">∞</tspan>
				<tspan style="font-size: 8.75px; " x="0" y="9.9300003">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="4.3497438" y="9.9300003">=</tspan>
				<tspan style="font-size: 8.75px; " x="10.344864" y="9.9300003">0</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-43.22,58.4)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑈</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-34.4,55.27)">
				<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
				<tspan style="font-size: 8.75px; " x="4.3759999" y="0">(</tspan>
				<tspan style="font-size: 8.75px; " x="7.2904158" y="0">𝑎</tspan>
				<tspan style="font-size: 8.75px; " x="11.68392" y="0">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="16.033665" y="0">+</tspan>
				<tspan style="font-size: 8.75px; " x="22.028784" y="0">𝑏</tspan>
				<tspan style="font-size: 8.75px; " x="26.142223" y="0">)</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-4.85,58.4)">
				<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
				<tspan style="font-size: 12.50px; " x="3.4758339" y="0">(</tspan>
				<tspan style="font-size: 12.50px; " x="7.6393328" y="0">𝑈</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,12.98,63.4)">
				<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
				<tspan style="font-size: 8.75px; " x="-1.38" y="9.1499996">𝑎</tspan>
				<tspan style="font-size: 8.75px; " x="3.013504" y="9.1499996">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="7.3632479" y="9.1499996">+</tspan>
				<tspan style="font-size: 8.75px; " x="13.358368" y="9.1499996">𝑏</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,33.73,58.4)">
				<tspan style="font-size: 12.50px; " x="0" y="0">+</tspan>
				<tspan style="font-size: 12.50px; " x="11.340221" y="0">𝑐</tspan>
				<tspan style="font-size: 12.50px; " x="16.528967" y="0">)</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,54.43,66.03)">
				<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
			</text>

		</g>
	</g>
</svg> for certain values of <svg style="vertical-align:-0.1254pt;width:7.9749999px;" id="M4" height="7.1750002" version="1.1" viewBox="0 0 7.9749999 7.1750002" width="7.9749999"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,7.175)">
		<g transform="translate(72,-66.26)">
			<text transform="matrix(1,0,0,-1,-71.95,66.44)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑎</tspan>
			</text>

		</g>
	</g>
</svg>, <svg style="vertical-align:-0.13794pt;width:7.4749999px;" id="M5" height="10.7375" version="1.1" viewBox="0 0 7.4749999 10.7375" width="7.4749999"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,10.7375)">
		<g transform="translate(72,-63.41)">
			<text transform="matrix(1,0,0,-1,-71.95,63.6)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑏</tspan>
			</text>

		</g>
	</g>
</svg>, and <svg style="vertical-align:-0.13794pt;width:7.3874998px;" id="M6" height="7.1875" version="1.1" viewBox="0 0 7.3874998 7.1875" width="7.3874998"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,7.1875)">
		<g transform="translate(72,-66.25)">
			<text transform="matrix(1,0,0,-1,-71.95,66.44)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑐</tspan>
			</text>

		</g>
	</g>
</svg>.

Ne&#351;e &#214;m&#252;r

On Reciprocal Series of Generalized Fibonacci Numbers with Subscripts in Arithmetic Progression

We study the behavior of the well-defined solutions of the max type difference equation <svg style="vertical-align:-3.49493pt;width:172.47501px;" id="M2" height="15.1125" version="1.1" viewBox="0 0 172.47501 15.1125" width="172.47501"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,15.1125)">
		<g transform="translate(72,-59.91)">
			<text transform="matrix(1,0,0,-1,-71.95,63.45)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-65.07,60.32)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="4.3497438" y="0">+</tspan>
				<tspan style="font-size: 8.75px; " x="10.344864" y="0">1</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-46.38,63.45)">
				<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
				<tspan style="font-size: 12.50px; " x="12.027886" y="0">m</tspan>
				<tspan style="font-size: 12.50px; " x="21.75522" y="0">a</tspan>
				<tspan style="font-size: 12.50px; " x="27.306553" y="0">x</tspan>
				<tspan style="font-size: 12.50px; " x="37.734055" y="0">{</tspan>
				<tspan style="font-size: 12.50px; " x="43.735493" y="0">1</tspan>
				<tspan style="font-size: 12.50px; " x="49.986996" y="0">/</tspan>
				<tspan style="font-size: 12.50px; " x="53.46283" y="0">𝑥</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,13.96,60.32)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,18.81,63.45)">
				<tspan style="font-size: 12.50px; " x="0" y="0">,</tspan>
				<tspan style="font-size: 12.50px; " x="5.2012482" y="0">𝐴</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,32.98,60.32)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,37.83,63.45)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,44.71,60.32)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
				<tspan style="font-size: 8.75px; " x="4.3497438" y="0">−</tspan>
				<tspan style="font-size: 8.75px; " x="10.344864" y="0">1</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,59.93,63.45)">
				<tspan style="font-size: 12.50px; " x="0" y="0">}</tspan>
			</text>

		</g>
	</g>
</svg>, <svg style="vertical-align:-1.76814pt;width:74.162498px;" id="M3" height="12.8875" version="1.1" viewBox="0 0 74.162498 12.8875" width="74.162498"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,12.8875)">
		<g transform="translate(72,-61.69)">
			<text transform="matrix(1,0,0,-1,-71.95,63.5)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑛</tspan>
				<tspan style="font-size: 12.50px; " x="9.6773224" y="0">=</tspan>
				<tspan style="font-size: 12.50px; " x="21.71771" y="0">0</tspan>
				<tspan style="font-size: 12.50px; " x="27.969212" y="0">,</tspan>
				<tspan style="font-size: 12.50px; " x="33.182961" y="0">1</tspan>
				<tspan style="font-size: 12.50px; " x="39.434464" y="0">,</tspan>
				<tspan style="font-size: 12.50px; " x="44.635712" y="0">…</tspan>
			</text>

		</g>
	</g>
</svg>, where the initial conditions are arbitrary nonzero real numbers and <svg style="vertical-align:-3.20526pt;width:32.400002px;" id="M4" height="14.75" version="1.1" viewBox="0 0 32.400002 14.75" width="32.400002"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,14.75)">
		<g transform="translate(72,-60.2)">
			<text transform="matrix(1,0,0,-1,-71.95,63.45)">
				<tspan style="font-size: 12.50px; " x="0" y="0">{</tspan>
				<tspan style="font-size: 12.50px; " x="6.00144" y="0">𝐴</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-56.98,60.32)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-52.14,63.45)">
				<tspan style="font-size: 12.50px; " x="0" y="0">}</tspan>
			</text>

		</g>
	</g>
</svg> is a period-two sequence of real numbers with <svg style="vertical-align:-3.20526pt;width:75.987503px;" id="M5" height="14.6875" version="1.1" viewBox="0 0 75.987503 14.6875" width="75.987503"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,14.6875)">
		<g transform="translate(72,-60.25)">
			<text transform="matrix(1,0,0,-1,-71.95,63.5)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝐴</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-62.99,60.37)">
				<tspan style="font-size: 8.75px; " x="0" y="0">𝑛</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-54.66,63.5)">
				<tspan style="font-size: 12.50px; " x="0" y="0">∈</tspan>
				<tspan style="font-size: 12.50px; " x="12.027886" y="0">[</tspan>
				<tspan style="font-size: 12.50px; " x="16.191385" y="0">0</tspan>
				<tspan style="font-size: 12.50px; " x="22.442884" y="0">,</tspan>
				<tspan style="font-size: 12.50px; " x="27.656635" y="0">∞</tspan>
				<tspan style="font-size: 12.50px; " x="39.234413" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg>.

&#304;brahim Yal&#231;&#305;nkaya

On the Max-Type Equation 
                    <svg style="vertical-align:-3.3907pt" height="16.4" version="1.1" viewBox="0 0 181.03751 16.4" width="181.03751" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.112)"><path id="x1D465" d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37&#xA;q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" /></g><g transform="matrix(.012,-0,0,-.012,9.563,16.2)"><path id="x1D45B" d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2&#xA;q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" /></g><g transform="matrix(.012,-0,0,-.012,15.536,16.2)"><path id="x2B" d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" /></g><g transform="matrix(.012,-0,0,-.012,22.52,16.2)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g><g transform="matrix(.017,-0,0,-.017,33.575,12.112)"><path id="x3D" d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,48.262,12.112)"><path id="x6D" d="M797 0h-214v26q46 5 58 17.5t12 63.5v167q0 116 -88 116q-48 0 -112 -52q3 -18 3 -42v-195q0 -46 11 -58t53 -17v-26h-214v26q48 5 59.5 17t11.5 60v172q0 115 -88 115q-47 0 -109 -52v-235q0 -47 10 -59.5t48 -17.5v-26h-211v26q50 5 62.5 17t12.5 60v207q0 48 -9 59.5&#xA;t-52 18.5v23q79 14 139 41v-81q3 2 29 20.5t44 29.5q45 28 81 28t66 -22t46 -61q25 20 83 57q39 26 76 26q59 0 93 -40t34 -113v-193q0 -49 10.5 -60.5t54.5 -16.5v-26z" /></g><g transform="matrix(.017,-0,0,-.017,62.184,12.112)"><path id="x61" d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5&#xA;t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" /></g><g transform="matrix(.017,-0,0,-.017,69.646,12.112)"><path id="x78" d="M474 0h-214v26q32 4 39 12t-5 28l-74 117q-39 -58 -64 -106q-16 -25 -10 -35t44 -16v-26h-186v26q46 6 64 17t48 49t85 120l-87 136q-23 36 -40 47t-58 16v26h199v-26q-31 -4 -36.5 -12.5t9.5 -29.5l59 -93q37 56 58 94q13 23 7 30t-40 11v26h183v-26q-47 -5 -65 -13.5&#xA;t-45 -39.5q-24 -29 -78 -110l97 -148q28 -43 46.5 -55.5t63.5 -18.5v-26z" /></g><g transform="matrix(.017,-0,0,-.017,83.347,12.112)"><path id="x7B" d="M293 -169q-145 0 -145 128q0 35 4 106t3 104q0 17 -2 28t-10 25.5t-28 23t-51 10.5v29q31 2 51 10.5t28 23t10 25.5t2 28q0 31 -4 101t-3 104q0 132 145 132v-28q-51 -7 -67.5 -30t-16.5 -63q0 -32 6.5 -99.5t6.5 -100.5q0 -97 -83 -115v-4q83 -20 83 -117&#xA;q0 -34 -6.5 -99.5t-6.5 -96.5q0 -41 16.5 -65.5t67.5 -31.5v-28z" /></g><g transform="matrix(.017,-0,0,-.017,89.246,12.112)"><use xlink:href="#x31"/></g><g transform="matrix(.017,-0,0,-.017,97.405,12.112)"><path id="x2F" d="M368 703l-264 -866h-60l265 866h59z" /></g><g transform="matrix(.017,-0,0,-.017,104.409,12.112)"><use xlink:href="#x1D465"/></g><g transform="matrix(.012,-0,0,-.012,113.912,16.2)"><use xlink:href="#x1D45B"/></g><g transform="matrix(.017,-0,0,-.017,120.512,12.112)"><path id="x2C" d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" /></g><g transform="matrix(.017,-0,0,-.017,127.21,12.112)"><path id="x1D434" d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" /></g><g transform="matrix(.012,-0,0,-.012,139.688,16.2)"><use xlink:href="#x1D45B"/></g><g transform="matrix(.017,-0,0,-.017,146.275,12.112)"><use xlink:href="#x1D465"/></g><g transform="matrix(.012,-0,0,-.012,155.775,16.2)"><use xlink:href="#x1D45B"/></g><g transform="matrix(.012,-0,0,-.012,161.748,16.2)"><path id="x2212" d="M535 230h-483v50h483v-50z" /></g><g transform="matrix(.012,-0,0,-.012,168.733,16.2)"><use xlink:href="#x31"/></g><g transform="matrix(.017,-0,0,-.017,175.075,12.112)"><path id="x7D" d="M283 255q-31 -2 -51 -10.5t-28 -23.5t-10 -27t-2 -30q0 -28 4 -97.5t4 -107.5q0 -128 -146 -128v28q50 7 67.5 31t17.5 63q0 33 -7 100t-7 98q0 96 84 117v4q-84 20 -84 115q0 34 7 102.5t7 98.5q0 40 -17.5 63t-67.5 30v28q28 0 50 -4t45.5 -16.5t37 -40t13.5 -68.5&#xA;q0 -37 -4 -106.5t-4 -98.5q0 -18 2 -30t10 -27t28 -23.5t51 -10.5v-29z" /></g></svg> with a Period-Two Parameter

About this journal

<p><em>Discrete Dynamics in Nature and Society</em> publishes research that links basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences.</p>


Journal profile

Meet the editorial board

<p>Chief Editor, Dr&nbsp;Renna, is an associate professor at the University of Basilicata, Italy. His research interests include manufacturing systems, production planning and enterprise networks.&nbsp;</p>


Editor spotlight

Submit to Special Issue

We currently have a number of Special Issues open for submission. Special Issues highlight emerging areas of research within a field, or provide a venue for a deeper investigation into an existing research area.

Special Issues

Author guidelines

Editorial board

Databases and indexing

Discrete Dynamics in Nature and Society - Table of contents 2012

Discrete Dynamics in Nature and Society | Hindawi

title

Discrete Dynamics in Nature and Society publishes research that links basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences.

description

https://images.hindawi.com/journals/ddns/ddns.banner.jpg

Discrete Dynamics in Nature and Society